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 A208215 Number of ways of dividing a 3 X n rectangle into rectangles of integer side lengths. 1
 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 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: ._   _   _   _ |_| |_| | | | | |_| | | |_| | | |_| |_| |_| |_| 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 * A025572 A093137 A214693 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 January 20 05:41 EST 2020. Contains 331067 sequences. (Running on oeis4.)