POLYOMINO TILINGS

Polyomino Tilings

Select polyominoes for a set (currently 1 or 2), for which tilings should be shown.

Then click "Show" button.

You may also see list of all polyomino sets for which data is available here.


I pentomino and I heptomino

Prime rectangles: ≥ 36.

Smallest rectangle tilings

Smallest rectangle (1x12):

Smallest square (7x7):

Rectangle tilings' solutions count (including symmetric)

Blue number - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Purple number - prime rectangle (unknown if weakly or strongly prime).

Red number - composite rectangle (which can be divided into two rectangles tileable by this set).

Gray number - it is unknown whether rectangle is prime or composite.

Question mark (?) - solution count is unknown.

Click on underlined numbers to view picture with one solution.

w \ h
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
N>0
1
0
2
0
0
3
0
0
0
4
0
0
0
0
5
0
0
0
0
0
6
0
0
0
0
0
0
7
0
0
0
0
0
8
24
8
0
0
0
0
2
0
40
0
9
0
0
0
0
3
2
58
12
16
10
0
0
0
0
4
8
88
188
299
852
11
0
0
0
0
5
0
190
4
120
≥1000
80
12
2
4
8
16
38
164
742
2508
≥1000
≥1000
≥1000
≥1000
13
0
0
0
0
73
2
1416
64
≥1000
≥1000
≥1000
≥1000
≥1000
14
0
0
0
0
110
326
2836
6926
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
15
0
0
0
0
152
324
5084
11328
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
16
0
0
0
0
196
86
8440
3766
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
17
3
9
27
81
486
2959
26018
147939
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
18
0
0
0
0
845
74
49222
13004
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
19
3
9
27
81
1519
10557
131985
845759
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
20
0
0
0
0
2334
5632
249486
653062
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1000
≥1
≥1
≥1
≥1
≥1
21
0
0
0
0
3296
12434
441132
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
22
4
16
64
256
5439
52062
1049234
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
23
0
0
0
0
8295
6284
1898576
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
24
6
36
216
1296
19750
245150
5491514
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
25
0
0
0
0
34139
95192
10687285
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
26
4
16
64
256
52801
596158
22680478
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
27
5
25
125
625
78714
1034163
48694023
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
28
0
0
0
0
111790
608680
87712494
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
29
10
100
1000
10000
253415
5475390
236705163
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
30
0
0
0
0
438764
1760112
456530040
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
31
10
100
1000
10000
774996
19405372
1.12850807×10¹⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
32
6
36
216
1296
1211250
20436288
2.32445676×10¹⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
33
5
25
125
625
1765488
33616279
4.46794627×10¹⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
34
15
225
3375
50625
3216148
121229279
1.08971399×10¹¹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
35
0
2
6
14
5173678
55494458
2.07263360×10¹¹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
36
20
400
8000
160000
10946037
517612296
5.38953370×10¹¹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
37
7
49
343
2401
18491669
407853653
1.08780478×10¹²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
38
15
225
3375
50625
28896017
1.36416269×10¹⁰
2.33289814×10¹²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
39
21
441
9261
194481
46201790
2.76484644×10¹⁰
5.28842252×10¹²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
40
6
48
342
2400
69287418
2.36862972×10¹⁰
1.01638454×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
41
35
1225
42875
1500625
152022491
1.29355114×10¹¹
2.58181759×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
42
8
80
728
6560
262331244
9.10025515×10¹⁰
5.13767580×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
43
35
1225
42875
1500625
458551009
4.50605543×10¹¹
1.21004222×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
44
28
784
21952
614656
730863623
6.34797865×10¹¹
2.61262957×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
45
21
483
10647
234255
1.09181120×10¹⁰
9.83355779×10¹¹
5.25938056×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
46
56
3136
175616
9834496
2.10813085×10¹⁰
3.19944738×10¹²
1.27228669×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
47
16
256
4096
65536
3.48732211×10¹⁰
2.56824975×10¹²
2.52021304×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
48
70
4900
343000
24010000
6.99605328×10¹⁰
1.29818892×10¹³
6.17967545×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
49
36
1368
50652
1874160
1.17024606×10¹¹
1.47892543×10¹³
1.29375394×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
50
56
3248
185192
10556000
1.84381697×10¹¹
3.66807381×10¹³
2.78989785×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
51
84
7056
592704
49787136
3.13311178×10¹¹
8.02442258×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
52
38
1444
54872
2085136
4.88371095×10¹¹
8.75797933×10¹³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
53
126
15876
2000376
252047376
1.03812476×10¹²
3.50702143×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
54
53
2809
148877
7890481
1.77937716×10¹²
3.67889100×10¹⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
55
126
16128
2048382
260144640
3.08453281×10¹²
1.21852169×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
56
120
14640
1771560
214358880
5.05289472×10¹²
2.03735405×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
57
95
9025
857375
81450625
7.74334215×10¹²
3.16478949×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
58
210
44100
9261000
1.94481000×10¹⁰
1.53485746×10¹³
9.34749046×10¹⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
59
91
8281
753571
68574961
2.57192510×10¹³
1.03271745×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
60
252
64008
16194276
4.09715208×10¹⁰
4.98572505×10¹³
3.68327108×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
61
174
30276
5268024
916636176
8.34498615×10¹³
5.24896735×10¹⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
62
222
49284
10941048
2.42891265×10¹⁰
1.33030604×10¹⁴
1.11641095×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
63
330
109560
36264690
1.20036127×10¹¹
2.37301997×10¹⁴
2.51830411×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
64
186
34596
6434856
1.19688321×10¹⁰
3.80511432×10¹⁴
3.26494771×10¹⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
65
462
214368
99252846
4.59540681×10¹¹
7.83326752×10¹⁴
1.05604895×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
66
265
70225
18609625
4.93155062×10¹⁰
1.33602882×10¹⁵
1.40555029×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
67
475
225625
107171875
5.09066406×10¹¹
2.30635682×10¹⁵
3.70908747×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
68
505
255025
128787625
6.50377506×10¹¹
3.90534071×10¹⁵
6.87481989×10¹⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
69
408
166464
67917312
2.77102632×10¹¹
6.14870318×10¹⁵
1.10196460×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
70
792
630434
500566182
3.97449550×10¹²
1.22461602×10¹⁶
2.98703535×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
71
451
203401
91733851
4.13719668×10¹¹
2.06527775×10¹⁶
4.03323374×10¹⁹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
72
938
879844
825293672
7.74125464×10¹²
3.90370281×10¹⁶
1.15920452×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
73
770
592900
456533000
3.51530410×10¹²
6.60378955×10¹⁶
1.90086923×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
74
883
779689
688465387
6.07914936×10¹²
1.06982269×10¹⁷
3.75550449×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
75
1298
1687400
2.19193389×10¹⁰
2.84732213×10¹³
1.97227858×10¹⁷
8.51429688×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
76
859
737881
633839779
5.44468370×10¹²
3.23140633×10¹⁷
1.25039890×10²¹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
77
1731
2999823
5.19569516×10¹⁰
8.99894403×10¹³
6.45055124×10¹⁷
3.48395151×10²¹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
78
1221
1490841
1.82031686×10¹⁰
2.22260688×10¹³
1.10094313×10¹⁸
5.38469150×10²¹
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
79
1821
3316041
6.03851066×10¹⁰
1.09961279×10¹⁴
1.90033589×10¹⁸
1.24701986×10²²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
80
2068
4280760
8.85689450×10¹⁰
1.83249147×10¹⁴
3.32156384×10¹⁸
2.45454526×10²²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
81
1742
3034564
5.28621048×10¹⁰
9.20857867×10¹³
5.36829390×10¹⁸
4.09699904×10²²
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
82
3031
9186961
2.78456787×10¹¹
8.44002524×10¹⁴
1.05971118×10¹⁹
1.03424318×10²³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
83
2080
4326400
8.99891200×10¹⁰
1.87177369×10¹⁴
1.79742288×10¹⁹
1.59153444×10²³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
84
3552
12623808
4.48523933×10¹¹
1.59360553×10¹⁵
3.33262149×10¹⁹
3.99267935×10²³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
85
3289
10824099
3.56112889×10¹¹
1.17161140×10¹⁵
5.73305586×10¹⁹
7.14953846×10²³
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
86
3563
12694969
4.52321745×10¹¹
1.61162237×10¹⁵
9.45937901×10¹⁹
1.37081694×10²⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
87
5100
26010000
1.32651000×10¹²
6.76520100×10¹⁵
1.77341000×10²⁰
3.08273068×10²⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
88
3822
14607684
5.58305682×10¹¹
2.13384431×10¹⁵
2.95639476×10²⁰
4.95221931×10²⁴
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
89
6584
43349056
2.85410184×10¹²
1.87914065×10¹⁶
5.73994414×10²⁰
1.24431156×10²⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
90
5369
28836899
1.54854152×10¹²
8.31566801×10¹⁵
9.86211800×10²⁰
2.11630175×10²⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
91
7115
50637455
3.60336136×10¹²
2.56415195×10¹⁶
1.70731011×10²¹
4.55365764×10²⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
92
8390
70392100
5.90589719×10¹²
4.95504774×10¹⁶
3.05714842×10²¹
9.26201057×10²⁵
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
93
7385
54538225
4.02764791×10¹²
2.97441798×10¹⁶
5.05610829×10²¹
1.60786157×10²⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
94
11684
136515856
1.59505126×10¹³
1.86365789×10¹⁷
9.82353161×10²¹
3.83624020×10²⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
95
9191
84492863
7.76658405×10¹²
7.13904406×10¹⁶
1.67879134×10²²
6.43766302×10²⁶
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
96
13700
187690000
2.57135300×10¹³
3.52275361×10¹⁷
3.06870848×10²²
1.48300850×10²⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
97
13760
189337600
2.60528537×10¹³
3.58487267×10¹⁷
5.37186079×10²²
2.80414771×10²⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
98
14500
210279000
3.04925579×10¹³
4.42172582×10¹⁷
9.02094889×10²²
5.33653141×10²⁷
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
99
20074
402965476
8.08912896×10¹³
1.62381174×10¹⁸
1.69790232×10²³
1.18347009×10²⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
100
16576
274796928
4.55530869×10¹³
7.55133521×10¹⁷
2.87239395×10²³
2.02698611×10²⁸
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
all
all
all
all
all
all
all
all
?
?
?
?
?
?
?
?
?
?
?
?

Formulas

$N(w; h)$ - number of ways to tile $w\times h$ rectangle (including symmetric solutions)

$T(w; h) = \begin{cases} 1, & N(w; h) \geq 1 \\ 0, & \text{else} \end{cases}$ - tileability function, $1$ if tiles rectangle, $0$ otherwise

$A(w; h) = \left(N(w; h)\right)^{\frac{1}{wh}}$ - average number of ways to tile cell in $w\times h$ rectangle (including symmetric solutions)

$G(T; x; y) = \sum_{w=1}^{\infty}\sum _{h=1}^{\infty}T(w; h)x^wy^h$ - bivariate generating function of $T(w; h)$

$G(A; x; y) = \sum_{w=1}^{\infty}\sum _{h=1}^{\infty}A(w; h)x^wy^h$ - bivariate generating function of $A(w; h)$

$G(N(1); x) = \frac{2x^{12} + 2x^{13} + 2x^{14} + 2x^{15} + 2x^{16} + x^{17} + x^{18}}{1 + x + x^2 + x^3 + x^4 - x^5 - x^6 - 3x^7 - 3x^8 - 3x^9 - 2x^{10} - 2x^{11} + x^{12} + x^{13} + 2x^{14} + 2x^{15} + 2x^{16} + x^{17} + x^{18}} \tag{1}$

$G(N(2); x) = \frac{4x^{12} + 8x^{13} + 12x^{14} + 16x^{15} + 20x^{16} + 17x^{17} + 10x^{18} - 8x^{19} - 26x^{20} - 44x^{21} - 58x^{22} - 69x^{23} - 73x^{24} - 70x^{25} - 56x^{26} - 43x^{27} - 31x^{28} - 20x^{29} - 10x^{30} - x^{31} + 4x^{32} + 4x^{33} + 4x^{34} + 4x^{35} + 4x^{36} + 3x^{37} + x^{38}}{1 + 2x + 3x^2 + 4x^3 + 5x^4 + 2x^5 - 2x^6 - 11x^7 - 20x^8 - 29x^9 - 32x^{10} - 32x^{11} - 19x^{12} - 2x^{13} + 25x^{14} + 48x^{15} + 68x^{16} + 76x^{17} + 77x^{18} + 62x^{19} + 42x^{20} + 13x^{21} - 11x^{22} - 31x^{23} - 44x^{24} - 51x^{25} - 48x^{26} - 42x^{27} - 32x^{28} - 23x^{29} - 14x^{30} - 5x^{31} + x^{32} + 3x^{33} + 4x^{34} + 4x^{35} + 4x^{36} + 3x^{37} + x^{38}} \tag{2}$

See Also

I pentomino and Z2 hexominoL pentomino and N pentomino