A247186 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)].

0, 0, 2, 3, 4, 7, 9, 12, 16, 20, 25, 31, 34, 42, 48, 53, 62, 71, 79, 88, 98, 105, 116, 128, 136, 146, 157, 169, 182, 195, 210, 228, 245, 259, 272, 289, 306, 322, 343, 362, 376, 395, 412, 436, 454, 478, 493, 509, 530, 555, 578, 602, 631, 652, 678, 708, 732, 759, 783, 808, 837, 870, 895

Offset: 0

Author

Derek Orr, Nov 22 2014

Keywords

• nonn

Comments

This is different from A247185 since here, a(i)+a(i) is included as a valid sum.

a(i)+a(j) and a(j)+a(i) are regarded as the same sum for all indices i and j.

a(n) <= A000217(n).

Examples

			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.
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.
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.
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.
		

Crossrefs

Cf. A247185.

Programs

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