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%I #10 Jul 22 2022 05:14:53
%S 1,2,3,8,27,78,219,649,1805,4987,13179,34331,87203,217281,532073,
%T 1278041,3025466,7046194,16192534,36706373,82197783,181900279,
%U 398099637,862217855,1848842707,3927404946,8267742253,17257223344,35726693834
%N Number of strings of numbers x(i=1..n) in 0..4 with sum i^2*x(i) equal to n^2*4
%C Column 4 of A183953
%H R. H. Hardin, <a href="/A183948/b183948.txt">Table of n, a(n) for n = 1..60</a>
%e Some solutions for n=6
%e ..0....4....2....3....4....0....3....2....2....0....4....0....2....3....4....2
%e ..2....1....2....3....4....3....0....1....4....2....1....3....1....4....1....1
%e ..2....2....1....2....3....0....1....0....2....1....1....1....1....0....4....4
%e ..2....2....4....0....0....2....2....1....0....1....1....3....2....4....4....1
%e ..2....2....1....3....1....4....4....2....0....3....3....3....1....1....0....2
%e ..1....1....1....1....2....0....0....2....3....1....1....0....2....1....1....1
%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, 4];
%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
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