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A076459
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Sum of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly n ways.
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7
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1, 57, 390, 1510, 4335, 10311, 21532, 40860, 72045, 119845, 190146, 290082, 428155, 614355, 860280, 1179256, 1586457, 2099025, 2736190, 3519390, 4472391, 5621407, 6995220, 8625300, 10545925, 12794301, 15410682, 18438490, 21924435, 25918635, 30474736, 35650032
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OFFSET
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1,2
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REFERENCES
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Fred. Schuh, Vragen betreffende een onbepaalde vergelijking, Nieuw Tijdschrift voor Wiskunde, 52 (1964-1965) 193-198.
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LINKS
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FORMULA
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a(n) = n*(n+1)*(2*n^3+2*n^2-2*n-1)/2.
G.f.: x*(1+51*x+63*x^2+5*x^3)/(1-x)^6.
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MAPLE
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seq(1/2*n*(n+1)*(2*n^3+2*n^2-2*n-1), n=1..35);
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MATHEMATICA
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CoefficientList[Series[(1 + 51 x + 63 x^2 + 5 x^3)/(1 - x)^6, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 30 2013 *)
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PROG
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(Magma) [n*(n+1)*(2*n^3+2*n^2-2*n-1)/2: n in [1..50]]; // Vincenzo Librandi, Dec 30 2013
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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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EXTENSIONS
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STATUS
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approved
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