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

Author

Alois P. Heinz, Dec 10 2012

Keywords

• nonn
• easy

Examples

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

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).

Crossrefs

Column m=4 of A116694.

Programs

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);

Formula

G.f.: see Maple program.