A247117 Number of tilings of a 10 X n rectangle using 2n pentominoes of shape I.

1, 1, 1, 1, 1, 8, 17, 28, 41, 56, 144, 317, 609, 1060, 1716, 3324, 6713, 13188, 24624, 43620, 80464, 153645, 296025, 562097, 1037921, 1920661, 3600832, 6820873, 12920804, 24211457, 45173688, 84493668, 158848825, 299451277, 562923960, 1055117520, 1976475968

Offset

0,6

Links

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

Wikipedia, Pentomino

Formula

G.f.: see Maple program.

Maple

gf:= -(x^10+x^8-x^6-2*x^5-x^4-x^3+1) *(x-1)^4 *(x^4+x^3+x^2+x+1)^4 / (x^35 +x^33 -2*x^31 -7*x^30 -2*x^29 -6*x^28 +x^27 +9*x^26 +22*x^25 +8*x^24 +15*x^23 -4*x^22 -15*x^21 -39*x^20 -12*x^19 -20*x^18 +6*x^17 +10*x^16 +45*x^15 +8*x^14 +19*x^13 -4*x^12 -4*x^11 -33*x^10 -6*x^9 -10*x^8 +x^7 -3*x^6 +12*x^5 +x^3 +x-1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..50);

Crossrefs

Cf. A174249, A233427, A003520 (5 X n), A247218 (15 X n).

Column k=5 of A250662.

Sequence in context: A264355 A028884 A322473 * A099358 A077222 A077221

Adjacent sequences: A247114 A247115 A247116 * A247118 A247119 A247120

Keyword

nonn,easy

Author

Alois P. Heinz, Nov 19 2014

Status

approved