A244877 Number of 4 X 4 traceless matrices of nonnegative integers with all row and column sums <= n.

1, 108, 3396, 49852, 447777, 2862384, 14265040, 58788720, 208577633, 655618172, 1864806372, 4877412332, 11877770177, 27199536768, 59037366080, 122252641280, 242826555969, 464730264172, 860261412132, 1545252073596, 2700999547873, 4605325025136, 7675844020560, 12529356938800

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]

Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Formula

G.f.: (1 + 95*x + 2070*x^2 + 13842*x^3 + 34416*x^4 + x^9 + 95*x^8 + 2070*x^7 + 13842*x^6 + 34416*x^5) / (1-x)^13.

a(n) = ((2+n)^2*(226800 + 1014480*n + 2137860*n^2 + 2775656*n^3 + 2422453*n^4 + 1468908*n^5 + 621705*n^6 + 180336*n^7 + 34191*n^8 + 3820*n^9 + 191*n^10)) / 907200. - Colin Barker, Jan 11 2017

Prog

(PARI) Vec((1 + 95*x + 2070*x^2 + 13842*x^3 + 34416*x^4 + x^9 + 95*x^8 + 2070*x^7 + 13842*x^6 + 34416*x^5) / (1-x)^13 + O(x^30)) \\ Colin Barker, Jan 11 2017

Crossrefs

Sequence in context: A221018 A338381 A269182 * A223153 A203028 A138784

Adjacent sequences: A244874 A244875 A244876 * A244878 A244879 A244880

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 08 2014

Status

approved