A361250 Number of tilings of a 5 X n rectangle using n pentominoes of shapes T, N, X.
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
Examples
a(10) = 2: .___________________. |___. |_. ._| .___| | |_. |___| |___|___ | | |_____|_| |___. |_| | .___| ._| |_. |___| |_|_____|_____|_____| ... and its mirror. . a(14) = 2: .___________________________. |___. |_. ._| |_. ._| .___| | |_. |___| |_. ._| |___|___ | | |_____|_| |_| |_| |___. |_| | .___| ._| |_. ._| |_. |___| |_|_____|_____|_|_____|_____| ... and its mirror. . a(16) = 2: ._______________________________. |___. |_. ._| .___|_. ._| .___| | |_. |___| |___| .___| |___|___ | | |_____|_| |___| ._|_| |___. |_| | .___| ._| |_____| ._| |_. |___| |_|_____|_____|_____|_____|_____| ... and its mirror. . a(17) = 2: ._________________________________. |___. |_. ._| |___. |_. ._| .___| | |_. |___| |_. ._| |___| |___|___ | | |_____|_| |_|_. ._| |_| |___. |_| | .___| ._| |_. |_|_. ._| |_. |___| |_|_____|_____|_____|_|_____|_____| ... and its mirror. .
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..5000
- 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).
Programs
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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);