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%I #18 Nov 28 2014 22:55:59
%S 0,0,2,3,4,7,9,12,16,20,25,31,34,42,48,53,62,71,79,88,98,105,116,128,
%T 136,146,157,169,182,195,210,228,245,259,272,289,306,322,343,362,376,
%U 395,412,436,454,478,493,509,530,555,578,602,631,652,678,708,732,759,783,808,837,870,895
%N a(0) = 0. a(n) is the number of repeating sums in the collection of all sums formed from [a(0), ... a(n-1)] + [a(0), ... a(n-1)].
%C This is different from A247185 since here, a(i)+a(i) is included as a valid sum.
%C a(i)+a(j) and a(j)+a(i) are regarded as the same sum for all indices i and j.
%C a(n) <= A000217(n).
%e a(1) is the number of repeating sums in the collection of all possible sums of [0] + [0]. There is only one possible sum here, 0+0. There are no repeats, so a(1) = 0.
%e a(2) is the number of repeating sums in the collection of all possible sums of [0,0] + [0,0]. The possible sums are 0+0, 0+0, and 0+0 (first+first, first+second, and second+second). There are two repeats, so a(2) = 2.
%e a(3) is the number of repeating sums in the collection of all possible sums of [0,0,2] + [0,0,2]. The possible sums are 0+0, 0+0, 0+2, 0+0, 0+2, and 2+2. There are 3 repeats, so a(3) = 3.
%e a(4) is the number of repeating sums in the collection of all possible sums of [0,0,2,3] + [0,0,2,3]. The possible sums are 0+0, 0+0, 0+2, 0+3, 0+0, 0+2, 0+3, 2+2, 2+3, and 3+3. There are 4 repeats, so a(4) = 4.
%o (PARI) v=[0];n=1;while(n<75,w=[];for(i=1,#v,for(j=i,#v,w=concat(w,v[i]+v[j])));v=concat(v,#w-#vecsort(w,,8));n++);v
%Y Cf. A247185.
%K nonn
%O 0,3
%A _Derek Orr_, Nov 22 2014
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