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

Author

Neal Gersh Tolunsky, May 25 2023

Keywords

• nonn

Examples

			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).
		

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

Crossrefs

Cf. A331614, A359634, A358537.

Programs

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