A183947 Number of strings of numbers x(i=1..n) in 0..3 with sum i^2*x(i) equal to n^2*3.

1, 1, 2, 4, 10, 26, 61, 147, 339, 771, 1721, 3770, 8123, 17233, 36041, 74322, 151368, 304614, 606305, 1194266, 2329462, 4501905, 8624652, 16386814, 30891283, 57801169, 107387377, 198165046, 363321016, 662012254, 1199130676, 2159720707

Offset: 1

Author

R. H. Hardin, Jan 08 2011

Keywords

• nonn

Comments

Column 3 of A183953

Examples

			All solutions for n=4
..3....2....1....0
..1....3....1....0
..1....2....3....0
..2....1....1....3
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..75

Programs

Mathematica

r[n_, k_, s_] := r[n, k, s] = Which[s < 0, 0, n == 0, If[s == 0, 1, 0], True, Sum[r[n - 1, k, s - c*n^2], {c, 0, k}]];
T[n_, k_] := r[n, k, k*n^2];
a[n_] := T[n, 3];
Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Jul 22 2022, after R. J. Mathar in A183953 *)