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A099903
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Sum of all matrix elements of N x N matrix M(i,j) = i^3+j^3, (i,j = 1..n). a(n) = 1/2 * (n^3)*(n+1)^2.
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7
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2, 36, 216, 800, 2250, 5292, 10976, 20736, 36450, 60500, 95832, 146016, 215306, 308700, 432000, 591872, 795906, 1052676, 1371800, 1764000, 2241162, 2816396, 3504096, 4320000, 5281250, 6406452, 7715736, 9230816, 10975050, 12973500
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Numerator of a(n)/n! - A099904(n).
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
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FORMULA
| a(n) = Sum[Sum[(i^3+j^3), {i, 1, n}], {j, 1, n}]. a(n) = 1/2 * (n^3)*(n+1)^2.
a(n) = 2*n*sum(k^3,k=1..n).[From Gary Detlefs, Oct 26 2011]
a(n) = (n^5 + 2n^4 + n^3)/2 \\ Charles R Greathouse IV, Oct 27 2011
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EXAMPLE
| a(3) = 1/2 * (2^3)*(2+1)^2 = 36
or
a(3) = (1^3+1^3) + (1^3+2^3) + (2^3+1^3) + (2^3+2^3) = 36.
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MAPLE
| a:=n->sum(sum(n^3/2, j=0..n), k=0..n): seq(a(n), n=1..30); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007
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MATHEMATICA
| Table[ Sum[i^3 + j^3, {i, n}, {j, n}], {n, 30}]
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PROG
| (PARI) a(n)=(n^5+2*n^4+n^3)/2 \\ Charles R Greathouse IV, Oct 27 2011
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CROSSREFS
| Cf. A099904, A019584, A098077.
Sequence in context: A141217 A206688 A025531 * A074426 A082636 A035603
Adjacent sequences: A099900 A099901 A099902 * A099904 A099905 A099906
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KEYWORD
| nonn,easy
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 29 2004
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