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A208215 Number of ways of dividing a 3 X n rectangle into rectangles of integer side lengths. 2
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

Table of n, a(n) for n=0..20.

J. Smith and H. Verrill, On dividing rectangles into rectangles.

Index entries for linear recurrences with constant coefficients, signature (15,-55,51).

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

Cf. A034999, A116694, A182275.

Sequence in context: A036352 A005569 A232910 * A337390 A025572 A093137

Adjacent sequences:  A208212 A208213 A208214 * A208216 A208217 A208218

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 May 16 14:39 EDT 2021. Contains 343949 sequences. (Running on oeis4.)