A363279 a(0)=1; a(1)=2. For n>1, a(n) is the number of contiguous groups in the sequence thus far whose sum is n.

1, 2, 1, 2, 1, 1, 2, 3, 1, 2, 4, 1, 3, 5, 4, 3, 5, 5, 2, 4, 6, 4, 4, 5, 2, 8, 5, 4, 7, 6, 6, 3, 8, 7, 5, 7, 5, 6, 11, 5, 6, 9, 11, 2, 6, 10, 8, 6, 6, 11, 7, 7, 10, 6, 10, 7, 6, 11, 11, 4, 9, 13, 6, 10, 11, 9, 8, 7, 9, 9, 10, 10, 6, 14, 10, 9, 8, 11, 7, 11, 12, 9, 11, 11, 10, 7

Offset

0,2

Links

Neal Gersh Tolunsky, Table of n, a(n) for n = 0..10000

Neal Gersh Tolunsky, Graph of first 10000 terms

Neal Gersh Tolunsky, Graph of first 100000 terms

Example

a(2)=1 because in the sequence thus far (1, 2), there is only one contiguous subsequence that sums to n=2: (2).
a(7)=3 because in the sequence thus far (1, 2, 1, 2, 1, 1, 2), there are three groups of consecutive terms that sum to n=7: (1, 2, 1, 2, 1); (2, 1, 2, 1, 1); (1, 2, 1, 1, 2).

Prog

(Python)
from collections import Counter
from itertools import count, islice
def agen(): # generator of terms
    yield from [1, 2]
    sumsn, c =  [2, 3], Counter([1, 2, 3])
    for n in count(2):
        an = c[n]
        yield an
        sumsn = [an] + [s + an for s in sumsn]
        c.update(sumsn)
print(list(islice(agen(), 86))) # Michael S. Branicky, May 25 2023

Crossrefs

Cf. A331614, A359634, A358537.

Sequence in context: A078349 A266476 A081327 * A205781 A357982 A280444

Adjacent sequences: A363276 A363277 A363278 * A363280 A363281 A363282

Keyword

nonn

Author

Neal Gersh Tolunsky, May 25 2023

Status

approved