A220298 Number of ways to cut a 5 X n rectangle into rectangles with integer sides.

1, 16, 650, 31484, 1613060, 84231996, 4427635270, 233276449488, 12300505521832, 648782777031100, 34223109012944482, 1805323555104984956, 95234889270955121716, 5023877415526067785580, 265022449692240368203598, 13980623266954069411358904

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

David A. Klarner and Spyros S. Magliveras, The number of tilings of a block with blocks, European Journal of Combinatorics 9 (1988), 317-330.

Joshua Smith and Helena Verrill, On dividing rectangles into rectangles

Formula

G.f.: see Maple program.

Example

a(1) = 16:
  ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._. ._.
  | | |_| | | | | | | |_| |_| |_| | | | | | | |_| |_| |_| | | |_|
  | | | | |_| | | | | |_| | | | | |_| |_| | | |_| |_| | | |_| |_|
  | | | | | | |_| | | | | |_| | | |_| | | |_| |_| | | |_| |_| |_|
  | | | | | | | | |_| | | | | |_| | | |_| |_| | | |_| |_| |_| |_|
  |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_| |_|
.

Maple

gf:= (39672144*x^10 -110891556*x^9 +124284414*x^8 -74544838*x^7 +26669637*x^6 -5961522*x^5 +841659*x^4 -73608*x^3 +3769*x^2 -100*x+1)/
(135762480*x^10 -326041524*x^9 +320708934*x^8 -170972730*x^7 +54776249*x^6 -11002298*x^5 +1395665*x^4 -109292*x^3 +4975*x^2 -116*x +1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..20);

Crossrefs

Column m=5 of A116694.

Sequence in context: A328274 A249950 A334734 * A222916 A346181 A197407

Adjacent sequences: A220295 A220296 A220297 * A220299 A220300 A220301

Keyword

nonn

Author

Alois P. Heinz, Dec 10 2012

Status

approved