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A058389
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Number of 3 X 3 matrices with nonnegative integer entries and all row sums equal to n, up to row and column permutation.
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7
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1, 3, 14, 44, 129, 316, 714, 1452, 2775, 4963, 8478, 13838, 21827, 33306, 49504, 71754, 101871, 141807, 194128, 261570, 347633, 456026, 591384, 758596, 963657, 1212861, 1513806, 1874440, 2304225, 2813030, 3412466, 4114608, 4933519
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| V. Jovovic, Illustration of initial terms
V. Jovovic, Number of m x m nonnegative integer matrices with all row sums equal to n, up to row and column permutation.
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FORMULA
| a(n)=1/6*(C(C(n + 2, 2) + 2, 3) + 3/2*floor((n + 2)/2)*(C(n + 2, 2) - floor((n + 2)/2)) + 3*C(floor((n + 2)/2) + 2, 3) + 2*floor(C(n + 2, 2)/3) + 2*C(C(n + 2, 2) - 3*floor(C(n + 2, 2)/3) + 2, 3)).
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MATHEMATICA
| a[n_] := (m = Mod[n, 6]; (n^3 + 9*n^2 + 39*n + 120)*n^3 + Which[m == 0, 12*(23*n^2 + 32*n + 24), m == 1 || m == 5, 249*n^2 + 303*n + 143, m == 2 || m == 4, 4*(69*n^2 + 96*n + 56), m == 3, 3*(83*n^2 + 101*n + 69)])/288; Table[a[n], {n, 0, 32}] (* From Jean-François Alcover, Oct 12 2011, after Vladeta Jovovic *)
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CROSSREFS
| Cf. A002817, A052282, A058390-A058392.
Cf. A050535, A050913, A058783, A058390, A058784, A058785, A058391, A058392, A001501, A058528
Sequence in context: A124650 A063903 A115005 * A059672 A032316 A032225
Adjacent sequences: A058386 A058387 A058388 * A058390 A058391 A058392
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KEYWORD
| nice,nonn,easy
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 24 2000
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EXTENSIONS
| More terms from Marc LeBrun (mlb(AT)well.com), Dec 11 2000
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