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A183956 Number of strings of numbers x(i=1..5) in 0..n with sum i^2*x(i) equal to n*25.

%I A183956 #11 Jul 22 2022 12:13:54
%S A183956 2,5,10,27,53,94,161,259,399,578,811,1120,1505,1985,2562,3267,4104,
%T A183956 5092,6249,7595,9146,10923,12948,15245,17831,20735,23980,27592,31597,
%U A183956 36020,40894,46252,52114,58520,65494,73076,81300,90195,99807,110163,121306
%N A183956 Number of strings of numbers x(i=1..5) in 0..n with sum i^2*x(i) equal to n*25.
%C A183956 Row 5 of A183953.
%H A183956 R. H. Hardin, <a href="/A183956/b183956.txt">Table of n, a(n) for n = 1..200</a>
%F A183956 Empirical: a(n)=a(n-1)+a(n-4)-a(n-5)+a(n-9)-a(n-10)-a(n-13)+a(n-14)+a(n-16)-a(n-17)-a(n-20)+a(n-21)-a(n-34)+a(n-35)+a(n-38)-a(n-39)-a(n-41)+a(n-42)+a(n-45)-a(n-46)+a(n-50)-a(n-51)-a(n-54)+a(n-55)
%e A183956 All solutions for n=3
%e A183956 ..0....1....1....0....1....2....3....3....0....0
%e A183956 ..0....2....2....0....2....0....1....1....0....0
%e A183956 ..2....2....0....0....1....0....3....2....3....1
%e A183956 ..2....3....1....0....2....3....1....0....3....1
%e A183956 ..1....0....2....3....1....1....1....2....0....2
%t A183956 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 A183956 T[n_, k_] := r[n, k, k*n^2];
%t A183956 a[n_] := T[5, n];
%t A183956 Table[a[n], {n, 1, 50}] (* _Jean-François Alcover_, Jul 22 2022, after _R. J. Mathar_ in A183953 *)
%K A183956 nonn
%O A183956 1,1
%A A183956 _R. H. Hardin_, Jan 08 2011