A359865 - OEIS

%I #13 Dec 22 2023 10:36:13

%S 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,

%T 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,

%U 0,5,1,6,1,2,3,0,6,2,4,4,2,4,3,2,2,5,2

%N 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.

%C 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.

%C This sequence has similarities with A308638: here we count geometric progressions, there arithmetic progressions.

%H Rémy Sigrist, <a href="/A359865/b359865.txt">Table of n, a(n) for n = 0..10000</a>

%H Rémy Sigrist, <a href="/A359865/a359865.png">Scatterplot of the first 250000 terms</a>

%H Rémy Sigrist, <a href="/A359865/a359865.txt">C program</a>

%e The first terms, alongside the corresponding k's, are:

%e   n   a(n)  k's

%e   --  ----  ------

%e    0     0  {}

%e    1     0  {}

%e    2     0  {}

%e    3     1  {1}

%e    4     1  {1}

%e    5     1  {2}

%e    6     1  {1}

%e    7     1  {1}

%e    8     2  {1, 2}

%e    9     0  {}

%e   10     0  {}

%e   11     1  {1}

%e   12     2  {1, 4}

%e   13     0  {}

%e   14     2  {3, 4}

%o (C) See Links section.

%Y Cf. A308638.

%K nonn

%O 0,9

%A _Rémy Sigrist_, Jan 16 2023