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A175827
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Partial sums of ceiling(n^2/10).
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2
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0, 1, 2, 3, 5, 8, 12, 17, 24, 33, 43, 56, 71, 88, 108, 131, 157, 186, 219, 256, 296, 341, 390, 443, 501, 564, 632, 705, 784, 869, 959, 1056, 1159, 1268, 1384, 1507, 1637, 1774, 1919, 2072, 2232, 2401, 2578, 2763, 2957, 3160, 3372, 3593, 3824, 4065, 4315
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = round((2*n+1)*(2*n^2 + 2*n + 27)/120).
a(n) = floor((2*n^3 + 3*n^2 + 28*n + 36)/60).
a(n) = ceiling((2*n^3 + 3*n^2 + 28*n - 9)/60).
a(n) = a(n-10) + (n+1)*(n-10) + 43.
G.f.: x*(1 - x + x^3 + x^7 - x^9 + x^10) / ( (1+x)*(x^4 + x^3 + x^2 + x + 1)*(x^4 - x^3 + x^2 - x + 1)*(x-1)^4 ).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-10) - 3*a(n-11) + 3*a(n-12) - a(n-13). (End)
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EXAMPLE
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a(10) = 0 + 1 + 1 + 1 + 2 + 3 + 4 + 5 + 7 + 9 + 10 = 43.
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MAPLE
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seq(ceil((2*n^3+3*n^2+28*n-9)/60), n=0..50)
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PROG
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(Magma) [Round((2*n+1)*(2*n^2+2*n+27)/120): n in [0..60]]; // Vincenzo Librandi, Jun 22 2011
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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