A359865 - OEIS

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.

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

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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, Table of n, a(n) for n = 0..10000

Rémy Sigrist, Scatterplot of the first 250000 terms

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 {}