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A129371
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a(n)=sum{k=0..floor(n/2), (n-k)^2}.
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2
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0, 1, 5, 13, 29, 50, 86, 126, 190, 255, 355, 451, 595, 728, 924, 1100, 1356, 1581, 1905, 2185, 2585, 2926, 3410, 3818, 4394, 4875, 5551, 6111, 6895, 7540, 8440, 9176, 10200, 11033, 12189, 13125, 14421, 15466, 16910, 18070
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Partial sums of A129370.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 21 2010]
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FORMULA
| G.f.: x(1+4x+5x^2+4x^3)/((1-x)(1-x^2)^3); a(n)=sum{k=floor((n+1)/2)..n, k^2};
a(n)= +a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +3*a(n-5) +a(n-6) -a(n-7). a(n) = 7*n^3/24+9*n^2/16+7*n/48+n*(-1)^n*(n-1)/16 . [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 21 2010]
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MATHEMATICA
| Accumulate[Table[n^2-(n-1)^2 (1-(-1)^n)/8, {n, 0, 50}]] (* From Harvey P. Dale, Oct 22 2011 *)
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CROSSREFS
| Sequence in context: A093836 A000328 A100438 * A194270 A194700 A130230
Adjacent sequences: A129368 A129369 A129370 * A129372 A129373 A129374
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 11 2007
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