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A304167
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a(n) = 3^n - 2^(n-1) + 2 (n>=1).
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2
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4, 9, 25, 75, 229, 699, 2125, 6435, 19429, 58539, 176125, 529395, 1590229, 4774779, 14332525, 43013955, 129074629, 387289419, 1161999325, 3486260115, 10459304629, 31378962459, 94138984525, 282421147875, 847271832229, 2541832273899, 7625530376125, 22876658237235, 68630108929429, 205890595223739
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OFFSET
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1,1
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COMMENTS
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For n>=2, a(n) is the number of vertices of the Sierpinski Gasket Rhombus graph SR(n) (see Theorem 2.1 in the D. Antony Xavier et al. reference).
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LINKS
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FORMULA
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G.f.: x*(4 - 15*x + 15*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).
a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>3.
(End)
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MAPLE
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seq(3^n-2^(n-1)+2, n = 1 .. 40);
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PROG
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(PARI) Vec(x*(4 - 15*x + 15*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)) + O(x^30)) \\ Colin Barker, May 10 2018
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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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STATUS
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approved
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