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A359034
a(n+1) is the sum of the number of terms in all groups of contiguous terms that add up to a(n); a(1)=1.
2
1, 1, 2, 3, 3, 4, 4, 5, 3, 5, 4, 6, 6, 7, 7, 8, 10, 11, 4, 7, 9, 9, 10, 12, 13, 14, 13, 15, 8, 11, 7, 10, 13, 16, 19, 18, 18, 19, 19, 20, 7, 11, 8, 12, 14, 14, 15, 9, 11, 9, 12, 15, 10, 14, 16, 20, 14, 17, 17, 18, 22, 22, 23, 22, 24, 23, 23, 24, 24, 25, 28, 27, 22
OFFSET
1,3
COMMENTS
If strongly smoothened, this sequence displays growth. This growth appears to be caused by the number of groups which is increasing by growing length of the sequence roughly proportional to n^(1/2). But the length of the groups appears to be nearly uninfluenced by this. - Thomas Scheuerle, Dec 14 2022
LINKS
Thomas Scheuerle, Scatter plot of a(n) per number of groups found. For n = 1...20000. This is the mean number of contiguous terms for each n.
EXAMPLE
a(17) is 10 because in the sequence so far (1, 1, 2, 3, 3, 4, 4, 5, 3, 5, 4, 6, 6, 7, 7, 8), these are the ways of adding contiguous terms to get a(16)=8: (2, 3, 3); (4, 4); (5, 3); (3, 5); (8). This is 10 terms in total, so a(17) is 10. Notice groups (5,3) and (3,5) overlap.
PROG
(MATLAB)
function a = A359034( max_n )
a = [1 1];
for n = 3:max_n
s = 1; e = 1; sm = 1; c = 0;
while e < n-1
while sm < a(n - 1) && e < (n - 1)
e = e + 1; sm = sm + a(e);
end
if sm == a(n - 1)
c = c + (e - s) + 1;
end
s = s + 1;
e = s; sm = a(s);
end
a(n) = c + 1;
end
end % Thomas Scheuerle, Dec 14 2022
CROSSREFS
Cf. A331614, A358919. Begins the same as A124056 (until a(13)).
Sequence in context: A217121 A368423 A253783 * A124056 A030396 A317658
KEYWORD
nonn
AUTHOR
Neal Gersh Tolunsky, Dec 12 2022
STATUS
approved