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 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
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 18 13:45 EDT 2024. Contains 376000 sequences. (Running on oeis4.)