cp's OEIS Frontend

A361250 Number of tilings of a 5 X n rectangle using n pentominoes of shapes T, N, X.

%I A361250 #19 May 02 2023 08:36:16
%S A361250 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,
%T A361250 306,204,544,342,1114,826,2038,1546,4144,3126,7452,6470,14538,12542,
%U A361250 27824,25994,53398,50244,103288,101306,195756,200120,380310,395802
%N A361250 Number of tilings of a 5 X n rectangle using n pentominoes of shapes T, N, X.
%H A361250 Alois P. Heinz, <a href="/A361250/b361250.txt">Table of n, a(n) for n = 0..5000</a>
%H A361250 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pentomino">Pentomino</a>
%H A361250 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,1,0,1,0,3,-1,6,-2,0,-6,-1).
%e A361250 a(10) = 2:
%e A361250    .___________________.
%e A361250    |___. |_. ._| .___| |
%e A361250    |_. |___| |___|___  |
%e A361250    | |_____|_| |___. |_|
%e A361250    | .___| ._| |_. |___|
%e A361250    |_|_____|_____|_____|  ... and its mirror.
%e A361250 .
%e A361250 a(14) = 2:
%e A361250    .___________________________.
%e A361250    |___. |_. ._| |_. ._| .___| |
%e A361250    |_. |___| |_. ._| |___|___  |
%e A361250    | |_____|_| |_| |_| |___. |_|
%e A361250    | .___| ._| |_. ._| |_. |___|
%e A361250    |_|_____|_____|_|_____|_____|  ... and its mirror.
%e A361250 .
%e A361250 a(16) = 2:
%e A361250    ._______________________________.
%e A361250    |___. |_. ._| .___|_. ._| .___| |
%e A361250    |_. |___| |___| .___| |___|___  |
%e A361250    | |_____|_| |___| ._|_| |___. |_|
%e A361250    | .___| ._| |_____| ._| |_. |___|
%e A361250    |_|_____|_____|_____|_____|_____|  ... and its mirror.
%e A361250 .
%e A361250 a(17) = 2:
%e A361250    ._________________________________.
%e A361250    |___. |_. ._| |___. |_. ._| .___| |
%e A361250    |_. |___| |_. ._| |___| |___|___  |
%e A361250    | |_____|_| |_|_. ._| |_| |___. |_|
%e A361250    | .___| ._| |_. |_|_. ._| |_. |___|
%e A361250    |_|_____|_____|_____|_|_____|_____|  ... and its mirror.
%e A361250 .
%p A361250 gf:= (x^14+4*x^13+2*x^11-4*x^10+x^9-3*x^8-x^6-x^4-x^3+1)/
%p A361250      (x^14+6*x^13+2*x^11-6*x^10+x^9-3*x^8-x^6-x^4-x^3+1):
%p A361250 a:= n-> coeff(series(gf, x, n+1), x, n):
%p A361250 seq(a(n), n=0..66);
%Y A361250 Cf. A174249, A343529, A349187, A352421, A358933.
%K A361250 nonn,easy
%O A361250 0,11
%A A361250 _Alois P. Heinz_, Apr 20 2023