A249762
Number of tilings of a 5 X n rectangle using n pentominoes of shapes F, I, L.
Original entry on oeis.org
1, 1, 3, 5, 13, 50, 133, 360, 875, 2254, 6336, 17331, 47199, 124476, 330344, 889454, 2400961, 6485476, 17392906, 46616158, 125153478, 336529923, 905611165, 2434088873, 6539233985, 17567977887, 47214493386, 126927551197, 341177175540, 916960655233
Offset: 0
a(4) = 13:
._______. ._______. ._______.
| | | | | | ._| ._| | | ._| |
| | | | | | |_. | | | | | | |
| | | | | | | |_| | | | | | |
| | | | | |_| ._| | | |_| | |
|_|_|_|_| (1) |___|___| (2) |_|___|_| (2)
._______. ._______. ._______.
| ._| | | | ._| ._| | ._|_. |
| | | | | | | | | | | | | | |
| | | | | | | | | | | | | | |
|_| | | | |_| |_| | |_| | |_|
|___|_|_| (4) |___|___| (2) |___|___| (2) .
A264812
Number of tilings of a 5 X n rectangle using n pentominoes of shapes P, I, X.
Original entry on oeis.org
1, 1, 3, 5, 13, 52, 123, 366, 909, 2444, 7108, 19157, 53957, 146826, 400704, 1115852, 3059907, 8475420, 23369304, 64225984, 177572352, 488839323, 1349102071, 3722419367, 10255126169, 28303059509, 78013005366, 215160477217, 593488173404, 1636220978049
Offset: 0
a(4) = 13:
._______. ._______. ._______. ._______.
| | | | | | | | | | | | | ._| |
| | | | | | ._| ._| | ._| | | |___| |
| | | | | |_| |_| | |_| | | | | |___|
| | | | | (1) | | | (4) | | | | (6) | ._| | (2)
|_|_|_|_| |___|___| |_ _|_|_| |_|_____| .
a(5) = 52:
._________.
| |_. |
| ._| |___|
|_|_ _| |
| |_| | (2) ...
|_____|___| .
A278330
Number of tilings of a 5 X n rectangle using n pentominoes of shapes P, U, X.
Original entry on oeis.org
1, 0, 2, 1, 12, 10, 59, 52, 276, 349, 1404, 1984, 7019, 11148, 35686, 62181, 182776, 339350, 942507, 1841208, 4887096, 9921685, 25442304, 53190380, 132928715, 284198328, 696276202, 1514363221, 3654567764, 8053235650, 19212546163, 42762014028, 101125071372
Offset: 0
a(2) = 2, a(3) = 1:
.___. .___. ._____.
| | | | | ._. |
| ._| |_. | |_| |_|
|_| | | |_| |_ _|
| | | | | |_| |
|___| |___| |_____| .
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Wikipedia, Pentomino
- Index entries for linear recurrences with constant coefficients, signature (0,2,2,8,4,21,-8,-4,-6,0,-16,-8).
Cf.
A079978,
A174249,
A233427,
A234312,
A234931,
A247124,
A247268,
A247443,
A249762,
A264765,
A264812.
-
a:= n-> (Matrix(12, (i, j)-> `if`(i+1=j, 1, `if`(i=12,
[-8, -16, 0, -6, -4, -8, 21, 4, 8, 2, 2, 0][j], 0)))^n.
<<1, 0, 2, 1, 12, 10, 59, 52, 276, 349, 1404, 1984>>)[1, 1]:
seq(a(n), n=0..35);
A273477
Number of tilings of a 7 X n rectangle using pentominoes of shapes W, U, X and monominoes.
Original entry on oeis.org
1, 1, 23, 1086, 13097, 261110, 5732276, 105028302, 2057123951, 40750196324, 789214306848, 15416490294168, 301533431477968, 5881271193704355, 114836714153318686, 2242611029205195253, 43780084385383228801, 854790034707804119211, 16689735991827528511674
Offset: 0
Showing 1-4 of 4 results.