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A372583
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a(n) = (3*n^5 + 5*n^3)/8.
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4
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1, 17, 108, 424, 1250, 3051, 6517, 12608, 22599, 38125, 61226, 94392, 140608, 203399, 286875, 395776, 535517, 712233, 932824, 1205000, 1537326, 1939267, 2421233, 2994624, 3671875, 4466501, 5393142, 6467608, 7706924, 9129375, 10754551, 12603392, 14698233
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OFFSET
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1,2
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COMMENTS
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Sum of pentagonal numbers in increasing groups 1, 5+12, 22+35+51, 70+92+117+145 etc.
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LINKS
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FORMULA
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G.f.: x*(1 + 11*x + 21*x^2 + 11*x^3 + x^4)/(1 - x)^6.
E.g.f.: exp(x)*x*(8 + 60*x + 80*x^2 + 30*x^3 + 3*x^4)/8. (End)
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EXAMPLE
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The first ten pentagonal numbers are 1, 5, 12, 22, 35, 51, 70, 92, 117, and 145. Taking them in groups, respectively, of 1, 2, 3, and 4, i.e., (1), (5, 12), (22, 35, 51), and (70, 92, 117, 145), and summing each group separately gives 1, 17, 108, 424.
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MATHEMATICA
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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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