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

3,2

Links

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

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

Column k=3 of A321615.

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