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A152257
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a(n) = (3^n - 1)^2*(3^n + 1)/16.
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1
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0, 1, 40, 1183, 32800, 893101, 24180520, 653473003, 17649155200, 476575627801, 12867977828200, 347439324082423, 9380897054183200, 253284538196972101, 6838685390919695080, 184644531291230453443, 4985402576490767372800, 134605871649898496094001
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = (3^n - 1)*(3^n - 1)*(3^n + 1)/16.
G.f.: x*(1-27*x^2)/((1-x)*(1-3*x)*(1-9*x)*(1-27*x)). - Robert Israel, Mar 18 2019
a(n) = 40*a(n-1) - 390*a(n-2) + 1080*a(n-3) - 729*a(n-4) for n>3. - Colin Barker, Mar 18 2019
E.g.f.: (1/16)*(exp(x) - exp(3*x) - exp(9*x) + exp(27*x)). (End)
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MAPLE
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MATHEMATICA
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Table[(9^n-1)*(3^n-1)/16, {n, 0, 30}]
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PROG
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(PARI) concat(0, Vec(x*(1 - 27*x^2) / ((1 - x)*(1 - 3*x)*(1 - 9*x)*(1 - 27*x)) + O(x^20))) \\ Colin Barker, Mar 18 2019
(Magma) [(9^n-1)*(3^n-1)/16: n in [0..40]]; // G. C. Greubel, May 22 2023
(SageMath) [(9^n-1)*(3^n-1)//16 for n in range(41)] # G. C. Greubel, May 22 2023
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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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