A220297 Number of ways to cut a 4 X n rectangle into rectangles with integer sides.

1, 8, 148, 3164, 70878, 1613060, 36911922, 846280548, 19415751782, 445550465628, 10225294476962, 234675373081668, 5385967300825942, 123612245431357148, 2837003283963428562, 65111601723938370628, 1494366038587416919782, 34296959750113321113308

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

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

Index entries for linear recurrences with constant coefficients, signature (44,-645,4280,-13840,20980,-11680).

Formula

G.f.: see Maple program.

Example

a(1) = 8:
  ._.  ._.  ._.  ._.  ._.  ._.  ._.  ._.
  | |  |_|  | |  | |  |_|  |_|  | |  |_|
  | |  | |  |_|  | |  |_|  | |  |_|  |_|
  | |  | |  | |  |_|  | |  |_|  |_|  |_|
  |_|  |_|  |_|  |_|  |_|  |_|  |_|  |_|
.

Maple

gf:= (3832*x^6 -8492*x^5 +6722*x^4 -2468*x^3 +441*x^2 -36*x+1) / (11680*x^6 -20980*x^5 +13840*x^4 -4280*x^3 +645*x^2 -44*x+1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..20);

Crossrefs

Column m=4 of A116694.

Sequence in context: A279127 A259991 A212732 * A307942 A116876 A218305

Adjacent sequences: A220294 A220295 A220296 * A220298 A220299 A220300

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 10 2012

Status

approved