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A220297 Number of ways to cut a 4 X n rectangle into rectangles with integer sides. 4
1, 8, 148, 3164, 70878, 1613060, 36911922, 846280548, 19415751782, 445550465628, 10225294476962, 234675373081668, 5385967300825942, 123612245431357148, 2837003283963428562, 65111601723938370628, 1494366038587416919782, 34296959750113321113308 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Dec 10 2012
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)