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A058389 Number of 3 X 3 matrices with nonnegative integer entries and all row sums equal to n, up to row and column permutation. 8
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; text; internal format)
OFFSET

0,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1000

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.

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)).

Empirical G.f.: -(x^8 + 3*x^7 + 14*x^6 + 12*x^5 + 15*x^4 + 9*x^3 + 5*x^2 + 1) / ((x-1)^7*(x+1)^3*(x^2+x+1)). - Colin Barker, Dec 27 2012

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}] (* Jean-Fran├žois Alcover, Oct 12 2011, after Vladeta Jovovic *)

PROG

(PARI) \\ See A318951 for RowSumMats

a(n)=RowSumMats(3, 3, n); \\ Andrew Howroyd, Sep 05 2018

CROSSREFS

Row 3 of A318951.

Cf. A002817, A052282, A058390, A058391, A058392.

Cf. A001501, A050535, A050913, A058528, A058783, A058784, A058785.

Sequence in context: A063903 A305009 A115005 * A261481 A059672 A302225

Adjacent sequences:  A058386 A058387 A058388 * A058390 A058391 A058392

KEYWORD

nice,nonn,easy

AUTHOR

Vladeta Jovovic, Nov 24 2000

EXTENSIONS

More terms from Marc LeBrun, Dec 11 2000

STATUS

approved

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Last modified January 20 07:59 EST 2020. Contains 331081 sequences. (Running on oeis4.)