%I #46 Apr 19 2023 09:04:41
%S 0,1,2,4,7,10,15,21,26,34,42,52,63,75,86,96,109,125,142,160,179,197,
%T 216,238,259,281,306,332,359,387,416,442,473,505,536,567,600,636,669,
%U 707,746,784,823,865,906,948,992,1036,1083,1129,1172,1222,1269,1321,1374,1428
%N a(n) is the number of distinct sums of one or more contiguous terms in the sequence thus far.
%H Winston de Greef, <a href="/A362040/b362040.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) <= A000217(n).
%e At n=1, there are no contiguous subsequences, so a(1)=0.
%e At n=2, there is one contiguous subsequence: [0], so a(2)=1.
%e At n=3, there are three contiguous subsequences: [0], [1] and [0, 1], but only two distinct sums (0 and 1), so a(3)=2.
%o (Python)
%o from itertools import islice
%o def gen_a():
%o seen = set()
%o sums = []
%o new = 0
%o while True:
%o for v in sums: seen.add(v + new)
%o sums = [v + new for v in sums]
%o sums.append(0)
%o new = len(seen)
%o yield new
%o print(list(islice(gen_a(), 60))) # _Winston de Greef_, Apr 15 2023
%Y Cf. A361798 (number of sums).
%Y Cf. A000217, A002048, A002049.
%K nonn
%O 1,3
%A _Neal Gersh Tolunsky_, Apr 15 2023
%E a(13)-a(15) corrected and more terms from _Winston de Greef_, Apr 15 2023