A054773 Number of nonnegative integer 4 X 4 matrices with sum of elements equal to n, up to rotational symmetry.

1, 4, 36, 204, 980, 3876, 13596, 42636, 122666, 326876, 817388, 1931540, 4346404, 9360540, 19390548, 38779380, 75136675, 141430680, 259292440, 463991880, 811990680, 1391975640, 2341057896, 3867821640, 6285222804, 10056336264

Offset: 0

Author

Vladeta Jovovic, May 19 2000

Keywords

• nonn

Links

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

Crossrefs

Row n=4 of A343874.

Cf. A008610.

Formula

G.f.: (x^16 - 4*x^15 + 28*x^14 - 12*x^13 + 76*x^12 + 60*x^11 + 196*x^10 - 44*x^9 + 422*x^8 - 44*x^7 + 196*x^6 + 60*x^5 + 76*x^4 - 12*x^3 + 28*x^2 - 4*x + 1)/ ((x - 1)^16*(x + 1)^8*(x^2 + 1)^4).