A247127 Number of tilings of a 5 X n rectangle using n pentominoes of shapes V, U, X, N.

1, 0, 0, 1, 4, 0, 9, 8, 24, 17, 78, 64, 227, 212, 664, 699, 2004, 2220, 6033, 7196, 18112, 22859, 54882, 72560, 166251, 229284, 505632, 721421, 1540532, 2264668, 4702135, 7092742, 14376450, 22165709, 44024116, 69154334, 134973515, 215459398, 414268932

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:= -(4*x^18 +4*x^17 -8*x^16 -3*x^15 -9*x^14 +2*x^13 -3*x^12 +5*x^11 -7*x^10 +x^9 -7*x^8 -x^6 -2*x^5 -x^3+1) / (32*x^26 +32*x^25 -32*x^24 +8*x^23 -120*x^22 +12*x^21 -124*x^20 +36*x^19 -123*x^18 +35*x^17 -106*x^16 +20*x^15 -62*x^14 -23*x^13 -22*x^12 -36*x^11 +5*x^10 -18*x^9 +13*x^8 -4*x^7 +8*x^6 +2*x^5 +4*x^4 +2*x^3-1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..50);

Crossrefs

Cf. A174249, A233427, A247126.

Sequence in context: A187189 A021248 A269843 * A277896 A376732 A195056

Adjacent sequences: A247124 A247125 A247126 * A247128 A247129 A247130

Keyword

nonn

Author

Alois P. Heinz, Nov 19 2014

Status

approved