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A208215 Number of ways of dividing a 3 X n rectangle into rectangles of integer side lengths. 3
1, 4, 34, 322, 3164, 31484, 314662, 3149674, 31544384, 315981452, 3165414034, 31710994234, 317682195692, 3182564368244, 31883205466534, 319408833724882, 3199866987994304, 32056562443839284, 321145602837871522, 3217266324544621714, 32230871396722195484 (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.
J. Smith and H. Verrill, On dividing rectangles into rectangles.
FORMULA
a(n) = 18*a(n-1) -100*a(n-2) +216*a(n-3) -153*a(n-4) with n>4 (see paper in Link lines, p. 1).
G.f.: 1+2*x*(2-13*x+16*x^2) / (1-15*x+55*x^2-51*x^3) = 1+2*x*(2-19*x+55*x^2-48*x^3) / (1-18*x+100*x^2-216*x^3+153*x^4). [Bruno Berselli, Apr 24 2012]
a(n) = 15*a(n-1) -55*a(n-2) +51*a(n-3) with n>3. [Bruno Berselli, Apr 24 2012]
EXAMPLE
For n=1 the a(1) = 4 ways to divide are:
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MATHEMATICA
Join[{1}, LinearRecurrence[{15, -55, 51}, {4, 34, 322}, 20]] (* Bruno Berselli, Apr 24 2012 *)
CROSSREFS
Sequence in context: A005569 A370171 A232910 * A337390 A025572 A093137
KEYWORD
nonn,easy
AUTHOR
Matthew C. Russell, Apr 23 2012
EXTENSIONS
More terms from Bruno Berselli, Apr 24 2012
a(0) added by Alois P. Heinz, Dec 10 2012
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)