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A361250
Number of tilings of a 5 X n rectangle using n pentominoes of shapes T, N, X.
3
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 8, 0, 18, 6, 16, 6, 48, 22, 74, 48, 182, 74, 306, 204, 544, 342, 1114, 826, 2038, 1546, 4144, 3126, 7452, 6470, 14538, 12542, 27824, 25994, 53398, 50244, 103288, 101306, 195756, 200120, 380310, 395802
OFFSET
0,11
LINKS
Wikipedia, Pentomino
Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,0,1,0,3,-1,6,-2,0,-6,-1).
EXAMPLE
a(10) = 2:
.___________________.
|___. |_. ._| .___| |
|_. |___| |___|___ |
| |_____|_| |___. |_|
| .___| ._| |_. |___|
|_|_____|_____|_____| ... and its mirror.
.
a(14) = 2:
.___________________________.
|___. |_. ._| |_. ._| .___| |
|_. |___| |_. ._| |___|___ |
| |_____|_| |_| |_| |___. |_|
| .___| ._| |_. ._| |_. |___|
|_|_____|_____|_|_____|_____| ... and its mirror.
.
a(16) = 2:
._______________________________.
|___. |_. ._| .___|_. ._| .___| |
|_. |___| |___| .___| |___|___ |
| |_____|_| |___| ._|_| |___. |_|
| .___| ._| |_____| ._| |_. |___|
|_|_____|_____|_____|_____|_____| ... and its mirror.
.
a(17) = 2:
._________________________________.
|___. |_. ._| |___. |_. ._| .___| |
|_. |___| |_. ._| |___| |___|___ |
| |_____|_| |_|_. ._| |_| |___. |_|
| .___| ._| |_. |_|_. ._| |_. |___|
|_|_____|_____|_____|_|_____|_____| ... and its mirror.
.
MAPLE
gf:= (x^14+4*x^13+2*x^11-4*x^10+x^9-3*x^8-x^6-x^4-x^3+1)/
(x^14+6*x^13+2*x^11-6*x^10+x^9-3*x^8-x^6-x^4-x^3+1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..66);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Apr 20 2023
STATUS
approved