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A054975 Number of nonnegative integer 3 X 3 matrices with no zero rows or columns and with sum of elements equal to n, up to row and column permutation. 2
1, 3, 13, 38, 97, 217, 453, 868, 1585, 2756, 4606, 7440, 11679, 17849, 26674, 39060, 56144, 79387, 110575, 151904, 206063, 276332, 366561, 481484, 626586, 808431, 1034636, 1314242, 1657500, 2076601, 2585262, 3199504, 3937370, 4819788 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

LINKS

Table of n, a(n) for n=3..36.

FORMULA

G.f.: x^3*(x^14 - 2*x^13 + x^12 - 3*x^11 + 4*x^10 - 3*x^9 + 4*x^8 - x^7 - 4*x^6 + 2*x^5 - x^4 - 5*x^3 - 4*x^2 - 1)/((x^4 - x^3 + x - 1)*(x^3 - 1)^3*(x + 1)^3*(x - 1)^5).

EXAMPLE

There are 3 nonnegative integer 3 X 3 matrices with no zero rows or columns and with sum of elements equal to 4, up to row and column permutation:

[0 0 1] [0 0 1] [0 0 1]

[0 0 1] [0 1 0] [0 1 0]

[1 1 0] [1 0 1] [2 0 0].

MAPLE

gf := x^3*(x^14 - 2*x^13 + x^12 - 3*x^11 + 4*x^10 - 3*x^9 + 4*x^8 - x^7 - 4*x^6 + 2*x^5 - x^4 - 5*x^3 - 4*x^2 - 1)/((x^4 - x^3 + x - 1)*(x^3 - 1)^3*(x+1)^3*(x - 1)^5): s := series(gf, x, 101): for i from 3 to 100 do printf(`%d, `, coeff(s, x, i)) od:

CROSSREFS

Cf. A052365.

Sequence in context: A147554 A076800 A277411 * A072790 A323009 A328703

Adjacent sequences: A054972 A054973 A054974 * A054976 A054977 A054978

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, May 28 2000

EXTENSIONS

More terms from James A. Sellers, May 29 2000

STATUS

approved

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Last modified November 29 08:40 EST 2022. Contains 358422 sequences. (Running on oeis4.)