A183955 Number of strings of numbers x(i=1..4) in 0..n with sum i^2*x(i) equal to n*16.

1, 1, 4, 8, 14, 21, 32, 48, 61, 82, 108, 139, 172, 210, 256, 311, 365, 427, 500, 582, 666, 759, 864, 982, 1097, 1228, 1372, 1529, 1688, 1860, 2048, 2253, 2457, 2677, 2916, 3172, 3430, 3705, 4000, 4316, 4629, 4966, 5324, 5703, 6084, 6486, 6912, 7363, 7813, 8287

Offset: 1

Author

R. H. Hardin, Jan 08 2011

Keywords

• nonn

Comments

Row 4 of A183953.

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A183953.

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[4, n];
Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Jul 22 2022, after R. J. Mathar in A183953 *)

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6) + a(n-16) - 2*a(n-17) + a(n-18) - a(n-20) + 2*a(n-21)-a(n-22).

Empirical g.f.: x*(1 - x + 3*x^2 + x^3 + x^4 + 2*x^5 + x^6 + 4*x^7 - 5*x^8 + 7*x^9 + x^10 + 5*x^12 - 3*x^13 + 3*x^14 + 4*x^15 - 4*x^16 + 4*x^17 - x^19 + 2*x^20 - x^21) / ((1 - x)^4*(1 + x)^2*(1 + x^2)^2*(1 + x^4)*(1 + x^8)). - Colin Barker, Apr 07 2018