A183946 - OEIS

A183946

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

%I #10 Jul 22 2022 05:20:08

%S 1,1,2,1,5,7,10,20,37,77,118,227,385,697,1191,2072,3489,5846,9862,

%T 16373,26897,44125,71991,116290,187653,300903,478422,761553,1200692,

%U 1893309,2961406,4630296,7188253,11155170,17211745,26490317,40633554,62126693

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

%C Column 2 of A183953

%H R. H. Hardin, <a href="/A183946/b183946.txt">Table of n, a(n) for n = 1..88</a>

%e All solutions for n=4

%e ..0

%e ..2

%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, 2];

%t Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Jul 22 2022, after _R. J. Mathar_ in A183953 *)

%K nonn

%O 1,3

%A _R. H. Hardin_, Jan 08 2011