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A086972
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a(n) = n*3^(n-1) + (3^n + 1)/2.
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3
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1, 3, 11, 41, 149, 527, 1823, 6197, 20777, 68891, 226355, 738113, 2391485, 7705895, 24712007, 78918989, 251105873, 796364339, 2518233179, 7942120025, 24988621541, 78452649023, 245818300271, 768835960421, 2400651060089
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A057711 (without leading zero). Second binomial transform of (1,1,3,3,5,5,7,7,9,9,11,11,...).
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LINKS
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FORMULA
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G.f.: (1-4*x+5*x^2)/((1-x)*(1-3*x)^2).
E.g.f.: (1/2)*( exp(x) + (2*x+1)*exp(3*x) ). - G. C. Greubel, Nov 24 2023
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MATHEMATICA
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Table[((2*n+3)*3^(n-1) +1)/2, {n, 0, 30}] (* G. C. Greubel, Nov 24 2023 *)
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PROG
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(PARI) Vec((1-4*x+5*x^2)/((1-x)*(1-3*x)^2) + O(x^40)) \\ Michel Marcus, Mar 08 2016
(SageMath) [((2*n+3)*3^(n-1) +1)//2 for n in range(31)] # G. C. Greubel, Nov 24 2023
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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