

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



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)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



