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A208215
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Number of ways of dividing a 3 X n rectangle into rectangles of integer side lengths.
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3
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1, 4, 34, 322, 3164, 31484, 314662, 3149674, 31544384, 315981452, 3165414034, 31710994234, 317682195692, 3182564368244, 31883205466534, 319408833724882, 3199866987994304, 32056562443839284, 321145602837871522, 3217266324544621714, 32230871396722195484
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OFFSET
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0,2
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LINKS
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FORMULA
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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]
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EXAMPLE
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For n=1 the a(1) = 4 ways to divide are:
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MATHEMATICA
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Join[{1}, LinearRecurrence[{15, -55, 51}, {4, 34, 322}, 20]] (* Bruno Berselli, Apr 24 2012 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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