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

0, 1, 2, 4, 7, 10, 15, 21, 26, 34, 42, 52, 63, 75, 86, 96, 109, 125, 142, 160, 179, 197, 216, 238, 259, 281, 306, 332, 359, 387, 416, 442, 473, 505, 536, 567, 600, 636, 669, 707, 746, 784, 823, 865, 906, 948, 992, 1036, 1083, 1129, 1172, 1222, 1269, 1321, 1374, 1428

Offset

1,3

Links

Winston de Greef, Table of n, a(n) for n = 1..10000

Formula

a(n) <= A000217(n).

Example

At n=1, there are no contiguous subsequences, so a(1)=0.
At n=2, there is one contiguous subsequence: [0], so a(2)=1.
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.

Prog

(Python)
from itertools import islice
def gen_a():
    seen = set()
    sums = []
    new = 0
    while True:
        for v in sums: seen.add(v + new)
        sums = [v + new for v in sums]
        sums.append(0)
        new = len(seen)
        yield new
print(list(islice(gen_a(), 60))) # Winston de Greef, Apr 15 2023

Crossrefs

Cf. A361798 (number of sums).

Cf. A000217, A002048, A002049.

Sequence in context: A007983 A049640 A179385 * A024668 A340248 A188951

Adjacent sequences: A362037 A362038 A362039 * A362041 A362042 A362043

Keyword

nonn

Author

Neal Gersh Tolunsky, Apr 15 2023

Extensions

a(13)-a(15) corrected and more terms from Winston de Greef, Apr 15 2023

Status

approved