cp's OEIS Frontend

A362040 a(n) is the number of distinct sums of one or more contiguous terms in the sequence thus far.

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