A247126 Number of tilings of a 5 X n rectangle using n pentominoes of shapes F, U, X, N.

1, 0, 0, 1, 2, 0, 1, 4, 4, 1, 14, 12, 17, 32, 64, 81, 138, 272, 489, 764, 1548, 2809, 5062, 9420, 17721, 32712, 60992, 114105, 213890, 398784, 747745, 1401476, 2624004, 4916369, 9218118, 17274340, 32378521, 60694768, 113785984, 213293721, 399856922, 749628208

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Pentomino

Formula

G.f.: see Maple program.

Maple

gf:= -(x+1) *(4*x^19 -4*x^18 +8*x^17 -4*x^16 +12*x^15 -12*x^14 +9*x^13 -5*x^12 -2*x^10 +5*x^9 -6*x^8 +10*x^7 -10*x^6 +8*x^5 -7*x^4 +4*x^3 -3*x^2 +3*x-1) / (4*x^23 +8*x^22 +12*x^21 +32*x^20 +8*x^19 +6*x^18 -15*x^17 -22*x^16 -9*x^15 -9*x^14 +13*x^13 +4*x^12 +22*x^11 -15*x^10 +x^9 -9*x^8 -x^7 +3*x^6 +3*x^5 +3*x^4 -2*x^3 -2*x+1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..50);

Crossrefs

Cf. A174249, A233427, A234931, A077909, A247127.

Sequence in context: A158417 A139435 A077909 * A342134 A349740 A327117

Adjacent sequences: A247123 A247124 A247125 * A247127 A247128 A247129

Keyword

nonn

Author

Alois P. Heinz, Nov 19 2014

Status

approved