A183954 Number of strings of numbers x(i=1..3) in 0..n with sum i^2*x(i) equal to n*9.

1, 2, 2, 3, 4, 6, 7, 9, 12, 14, 17, 19, 22, 25, 29, 32, 36, 41, 45, 50, 54, 59, 64, 70, 75, 81, 88, 94, 101, 107, 114, 121, 129, 136, 144, 153, 161, 170, 178, 187, 196, 206, 215, 225, 236, 246, 257, 267, 278, 289, 301, 312, 324, 337, 349, 362, 374, 387, 400, 414, 427, 441

Offset

1,2

Comments

Row 3 of A183953.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-9) - 2*a(n-10) + a(n-11).

Empirical g.f.: x*(1 + x)*(1 - x + x^3 - x^4 + 2*x^5 - 3*x^6 + 4*x^7 - 3*x^8 + x^9) / ((1 - x)^3*(1 + x + x^2)*(1 + x^3 + x^6)). - Colin Barker, Apr 07 2018

Example

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

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[3, n];
Table[a[n], {n, 1, 62}] (* Jean-François Alcover, Jul 22 2022, after R. J. Mathar in A183953 *)

Crossrefs

Cf. A183953.

Sequence in context: A119604 A036806 A039908 * A266747 A246762 A093950

Adjacent sequences: A183951 A183952 A183953 * A183955 A183956 A183957

Keyword

nonn

Author

R. H. Hardin, Jan 08 2011

Status

approved