A244865 Number of 3 X 3 symmetric matrices with row and column sums <= n.

1, 14, 85, 336, 1023, 2610, 5860, 11942, 22555, 40068, 67677, 109578, 171157, 259196, 382096, 550116, 775629, 1073394, 1460845, 1958396, 2589763, 3382302, 4367364, 5580666, 7062679, 8859032, 11020933, 13605606, 16676745, 20304984, 24568384, 29552936, 35353081, 42072246, 49823397, 58729608

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R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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 (6,-14,14,0,-14,14,-6,1).

Formula

G.f.: (1 + 8*x + 15*x^2 + 8*x^3 + x^4) / ((1 - x)^7*(1 + x)).

From Colin Barker, Jan 11 2017: (Start)

a(n) = (15*(127+(-1)^n) + 6432*n + 8936*n^2 + 6480*n^3 + 2570*n^4 + 528*n^5 + 44*n^6) / 1920.

a(n) = 6*a(n-1) - 14*a(n-2) + 14*a(n-3) - 14*a(n-5) + 14*a(n-6) - 6*a(n-7) + a(n-8) for n>7.

(End)

Prog

(PARI) Vec((1 + 8*x + 15*x^2 + 8*x^3 + x^4) / ((1 - x)^7*(1 + x)) + O(x^40)) \\ Colin Barker, Jan 11 2017

Crossrefs

Sequence in context: A341854 A025607 A272103 * A059600 A206621 A213121

Adjacent sequences: A244862 A244863 A244864 * A244866 A244867 A244868

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 07 2014

Status

approved