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

%I A183955 #13 Jul 22 2022 05:15:02
%S A183955 1,1,4,8,14,21,32,48,61,82,108,139,172,210,256,311,365,427,500,582,
%T A183955 666,759,864,982,1097,1228,1372,1529,1688,1860,2048,2253,2457,2677,
%U A183955 2916,3172,3430,3705,4000,4316,4629,4966,5324,5703,6084,6486,6912,7363,7813,8287
%N A183955 Number of strings of numbers x(i=1..4) in 0..n with sum i^2*x(i) equal to n*16.
%C A183955 Row 4 of A183953.
%H A183955 R. H. Hardin, <a href="/A183955/b183955.txt">Table of n, a(n) for n = 1..200</a>
%F A183955 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).
%F A183955 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
%e A183955 All solutions for n=3:
%e A183955 ..2....3....0....1
%e A183955 ..3....1....0....1
%e A183955 ..2....1....0....3
%e A183955 ..1....2....3....1
%t A183955 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 A183955 T[n_, k_] := r[n, k, k*n^2];
%t A183955 a[n_] := T[4, n];
%t A183955 Table[a[n], {n, 1, 50}] (* _Jean-François Alcover_, Jul 22 2022, after _R. J. Mathar_ in A183953 *)
%Y A183955 Cf. A183953.
%K A183955 nonn
%O A183955 1,3
%A A183955 _R. H. Hardin_, Jan 08 2011