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.

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

Offset: 3

Author

Vladeta Jovovic, May 28 2000

Keywords

• easy
• nonn

Examples

			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].
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 3..1000

Crossrefs

Column k=3 of A321615.

Cf. A052365.

Programs

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:

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).

Extensions

More terms from James Sellers, May 29 2000