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A359865 a(n) is the number of k > 0 such that n-1-2*k >= 0 and a(n-1-2*k) * a(n-1) = a(n-1-k)^2. 1
0, 0, 0, 1, 1, 1, 1, 1, 2, 0, 0, 1, 2, 0, 2, 0, 3, 2, 3, 2, 1, 2, 2, 1, 0, 2, 3, 1, 0, 2, 2, 4, 4, 2, 3, 1, 4, 1, 1, 1, 4, 3, 1, 1, 5, 0, 2, 4, 4, 2, 1, 3, 0, 2, 0, 3, 1, 4, 2, 1, 5, 0, 3, 1, 5, 0, 4, 3, 0, 5, 1, 6, 1, 2, 3, 0, 6, 2, 4, 4, 2, 4, 3, 2, 2, 5, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,9
COMMENTS
In other words, a(n) gives the number of geometric progressions (a(n-1-2*k), a(n-1-k), a(n-1)) of the form (x, x*y, x*y^2) or (x*y^2, x*y, x) with x, y >= 0.
This sequence has similarities with A308638: here we count geometric progressions, there arithmetic progressions.
LINKS
Rémy Sigrist, C program
EXAMPLE
The first terms, alongside the corresponding k's, are:
n a(n) k's
-- ---- ------
0 0 {}
1 0 {}
2 0 {}
3 1 {1}
4 1 {1}
5 1 {2}
6 1 {1}
7 1 {1}
8 2 {1, 2}
9 0 {}
10 0 {}
11 1 {1}
12 2 {1, 4}
13 0 {}
14 2 {3, 4}
PROG
(C) See Links section.
CROSSREFS
Cf. A308638.
Sequence in context: A360670 A347992 A317581 * A035217 A357237 A277808
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jan 16 2023
STATUS
approved

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Last modified July 15 01:36 EDT 2024. Contains 374323 sequences. (Running on oeis4.)