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%I #10 Jul 22 2022 05:15:15
%S 1,2,4,14,53,180,656,2195,7250,23044,71123,213368,624425,1784399,
%T 4986210,13657266,36691985,96863639,251472815,642811767,1619203005,
%U 4022796235,9864987052,23894800443,57205375668,135438579331,317296680619
%N Number of strings of numbers x(i=1..n) in 0..5 with sum i^2*x(i) equal to n^2*5
%C Column 5 of A183953
%H R. H. Hardin, <a href="/A183949/b183949.txt">Table of n, a(n) for n = 1..54</a>
%e All solutions for n=4
%e ..0....1....0....3....3....3....4....2....4....1....5....0....3....5
%e ..3....1....4....0....1....4....3....3....2....5....4....0....5....0
%e ..4....3....0....5....1....5....0....2....4....3....3....0....1....3
%e ..2....3....4....2....4....1....4....3....2....2....2....5....3....3
%t 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 T[n_, k_] := r[n, k, k*n^2];
%t a[n_] := T[n, 5];
%t Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Jul 22 2022, after _R. J. Mathar_ in A183953 *)
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 08 2011