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A139594
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Number of different n X n symmetric matrices with nonnegative entries summing to 4. Also number of symmetric oriented graphs with 4 arcs on n points.
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4
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0, 1, 9, 39, 116, 275, 561, 1029, 1744, 2781, 4225, 6171, 8724, 11999, 16121, 21225, 27456, 34969, 43929, 54511, 66900, 81291, 97889, 116909, 138576, 163125, 190801, 221859, 256564, 295191, 338025, 385361, 437504, 494769, 557481, 625975, 700596
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OFFSET
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0,3
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COMMENTS
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a(n) is also the number of semistandard Young tableaux over all partitions of 4 with maximal element <= n. - Alois P. Heinz, Mar 22 2012
Starting from 1 the partial sums give A244864. - J. M. Bergot, Sep 17 2016
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n) = coefficient of X^4 in 1/((1-X)^m*(1-X^2)^binomial(m,2)).
Conjecture: a(n) = (n^2*(7+5*n^2))/12. G.f.: x*(1+x)*(1+3*x+x^2)/(1-x)^5. [Colin Barker, Mar 18 2012]
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EXAMPLE
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From Michael B. Porter, Sep 18 2016: (Start)
The nine 2 X 2 matrices summing to 4 are:
4 0 3 0 2 0 1 0 0 0 2 1 1 1 0 1 0 2
0 0 0 1 0 2 0 3 0 4 1 0 1 1 1 2 2 0
(End)
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MAPLE
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dd := proc(n, m) coeftayl(1/((1-X)^m*(1-X^2)^binomial(m, 2)), X=0, n); seq(dd(4, m), m=0..N);
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CROSSREFS
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For 3 in place of 4 this gives A005900.
Row n=4 of A210391. - Alois P. Heinz, Mar 22 2012
Sequence in context: A299280 A023163 A054121 * A034263 A060929 A212143
Adjacent sequences: A139591 A139592 A139593 * A139595 A139596 A139597
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KEYWORD
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easy,nonn
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AUTHOR
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Marc A. A. van Leeuwen, Jun 12 2008
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STATUS
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approved
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