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1, 121, 1068, 4720, 14705, 36981, 80416, 157368, 284265, 482185, 777436, 1202136, 1794793, 2600885, 3673440, 5073616, 6871281, 9145593, 11985580, 15490720, 19771521, 24950101, 31160768, 38550600, 47280025, 57523401, 69469596, 83322568, 99301945
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OFFSET
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1,2
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COMMENTS
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Geometrically, the partial sums of A092182 may be interpreted as 5-dimensional hexacosichoronal hyperpyramidal numbers. The hexacosichoron is a convex regular 4-D polytope with Schlaefli symbol {3,3,5}.
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LINKS
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FORMULA
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G.f.: x*(1 + 115*x + 357*x^2 + 107*x^3) / (1 - x)^6.
a(n) = (n*(12 + n - 64*n^2 + 5*n^3 + 58*n^4)) / 12.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)
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PROG
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(PARI) Vec(x*(1 + 115*x + 357*x^2 + 107*x^3) / (1 - x)^6 + O(x^40)) \\ Colin Barker, Aug 15 2018
(PARI) a(n) = (n*(12 + n - 64*n^2 + 5*n^3 + 58*n^4)) / 12 \\ Colin Barker, Aug 15 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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