A052366 Number of nonnegative integer 4 X 4 matrices with sum of elements equal to n, under row and column permutations.

1, 1, 4, 10, 33, 78, 224, 549, 1403, 3292, 7677, 16934, 36581, 75732, 152949, 298784, 569636, 1056500, 1916502, 3396630, 5901524, 10051384, 16820192, 27664756, 44795247, 71442327, 112366941, 174384376, 267289440, 404838044, 606375995

Offset: 0

Author

Vladeta Jovovic, Mar 08 2000

Keywords

• nonn

Links

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

Crossrefs

Row 4 of A318795.

Cf. A002724, A053307, A052365.

Formula

G.f.: (x^34 - 4*x^33 + 6*x^32 - x^31 + 3*x^30 - 11*x^29 + 33*x^28 - 19*x^27 + 81*x^26 - 52*x^25 + 152*x^24 - 36*x^23 + 255*x^22 - 130*x^21 + 367*x^20 - 84*x^19 + 350*x^18 - 94*x^17 + 350*x^16 - 84*x^15 + 367*x^14 - 130*x^13 + 255*x^12 - 36*x^11 + 152*x^10 - 52*x^9 + 81*x^8 - 19*x^7 + 33*x^6 - 11*x^5 + 3*x^4 - x^3 + 6*x^2 - 4*x + 1)/((x^10 + x^9 - x^7 - x^6 + x^4 + x^3 - x - 1)*(x^6 - 1)^2*(x^2 + 1)^3*(x^2 - 1)^4*(x^2 + x + 1)^2*(x + 1)*(x - 1)^9).