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%I #7 Nov 28 2014 22:56:43
%S 0,0,2,6,23,80,302,1160,4504,17087,66327
%N a(0) = 0. a(n) is the number of repeating sums made from [a(0), ... a(n-1)] + [a(0), ... a(n-1)] + ... + [a(0), ... a(n-1)], where [a(0), ... a(n-1)] is repeated n times.
%C a(i)+a(j) and a(j)+a(i) are considered to be the same sum for all indices i and j.
%e a(1) is the number of repeating sums made from [0]. No sums can be made from this because 0 is not being added to anything. So a(1) = 0.
%e a(2) is the number of repeating sums made from [0,0] + [0,0]. The possible sums are 0+0, 0+0, and 0+0, so a(2) = 2.
%e a(3) is the number of repeating sums made from [0,0,2] + [0,0,2] + [0,0,2]. The possible sums are 0+0+0, 0+0+0, 0+0+2, 0+0+0, 0+0+2, 0+2+2, 0+0+0, 0+0+2, 0+2+2, and 2+2+2. There are 6 repeating sums so a(3) = 6.
%e a(4) is the number of repeating sums made from [0,0,2,6] + [0,0,2,6] + [0,0,2,6] + [0,0,2,6]. There are 23 repeating sums, so a(4) = 23.
%K nonn,more,hard
%O 0,3
%A _Derek Orr_, Nov 26 2014