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A055005
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Number of nonnegative integer 3 X 3 matrices with no zero rows or columns and with sum of elements equal to n.
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0
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1, 0, 0, 6, 63, 306, 1038, 2844, 6750, 14437, 28521, 52911, 93258, 157509, 256581, 405171, 622719, 934542, 1373158, 1979820, 2806281, 3916812, 5390496, 7323822, 9833604, 13060251, 17171415, 22366045, 28878876, 36985383, 47007231
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| Number of nonnegative integer p X q matrices with no zero rows or columns and with sum of elements equal to n is Sum_{k=0...q} (-1)^k*C(q, k)*m(p, q-k, n) where m(p, q, n)=Sum_{k=0..p} (-1)^k*C(p, k)*C((p-k)*q+n-1, n).
For p=q=3 we get a(n)=C(n + 8, 8) - 6*C(n + 5, 5) + 9*C(n + 3, 3) + 6*C(n + 2, 2) - 18*C(n + 1, 1) + 9=(1/8!)*(n^8 + 36*n^7 + 546*n^6 + 2520*n^5 - 7791*n^4 - 43596*n^3 + 148364*n^2 - 140400*n + 40320).
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CROSSREFS
| Cf. A054688, A054974, A054975.
Sequence in context: A190726 A121251 A158987 * A027811 A027950 A184447
Adjacent sequences: A055002 A055003 A055004 * A055006 A055007 A055008
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), May 30 2000
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