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A247126
Number of tilings of a 5 X n rectangle using n pentominoes of shapes F, U, X, N.
4
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 19 2014
STATUS
approved