A055007 Number of nonnegative integer 4 X 4 matrices with no zero rows or columns and with sum of elements equal to n.

1, 0, 0, 0, 24, 528, 4648, 26224, 112666, 401424, 1246000, 3476368, 8905432, 21266208, 47875272, 102482048, 210000931, 414160240, 789572072, 1460372624, 2628456428, 4615495808, 7924479264, 13328517504, 21997272036, 35674700896, 56926058920, 89477437120

Offset

0,5

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Formula

Number of nonnegative integer p X q matrices with no zero rows or columns and with sum of elements equal to n is Sum_{k=0...q} (-1)^k*C(q, k)*m(p, q-k, n) where m(p, q, n)=Sum_{k=0..p} (-1)^k*C(p, k)*C((p-k)*q+n-1, n).

For p = q = 4 we get a(n) = (1/15!)*(n^15 + 120*n^14 + 6580*n^13 + 218400*n^12 + 4637542*n^11 + 61261200*n^10 + 423591740*n^9 + 164392800*n^8 - 17247717487*n^7 - 47940252360*n^6 + 346941238280*n^5 + 557885764800*n^4 - 4897231459056*n^3 + 8643549191040*n^2 - 5894285241600*n + 1307674368000).

G.f.: -(16*x^15 -192*x^14 +1040*x^13 -3356*x^12 +7200*x^11 -10952*x^10 +12544*x^9 -11712*x^8 +9664*x^7 -7088*x^6 +4224*x^5 -1844*x^4 +560*x^3 -120*x^2 +16*x -1) / (x -1)^16. - Colin Barker, Jul 11 2013

Crossrefs

Cf. A054688, A054974, A054975, A052366.

Sequence in context: A289833 A242524 A264956 * A014907 A233636 A121905

Adjacent sequences: A055004 A055005 A055006 * A055008 A055009 A055010

Keyword

easy,nonn

Author

Vladeta Jovovic, May 30 2000

Extensions

More terms from James A. Sellers, May 31 2000

Status

approved