This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A359865 #13 Dec 22 2023 10:36:13
%S A359865 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 A359865 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 A359865 0,5,1,6,1,2,3,0,6,2,4,4,2,4,3,2,2,5,2
%N 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.
%C A359865 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 A359865 This sequence has similarities with A308638: here we count geometric progressions, there arithmetic progressions.
%H A359865 Rémy Sigrist, <a href="/A359865/b359865.txt">Table of n, a(n) for n = 0..10000</a>
%H A359865 Rémy Sigrist, <a href="/A359865/a359865.png">Scatterplot of the first 250000 terms</a>
%H A359865 Rémy Sigrist, <a href="/A359865/a359865.txt">C program</a>
%e A359865 The first terms, alongside the corresponding k's, are:
%e A359865 n a(n) k's
%e A359865 -- ---- ------
%e A359865 0 0 {}
%e A359865 1 0 {}
%e A359865 2 0 {}
%e A359865 3 1 {1}
%e A359865 4 1 {1}
%e A359865 5 1 {2}
%e A359865 6 1 {1}
%e A359865 7 1 {1}
%e A359865 8 2 {1, 2}
%e A359865 9 0 {}
%e A359865 10 0 {}
%e A359865 11 1 {1}
%e A359865 12 2 {1, 4}
%e A359865 13 0 {}
%e A359865 14 2 {3, 4}
%o A359865 (C) See Links section.
%Y A359865 Cf. A308638.
%K A359865 nonn
%O A359865 0,9
%A A359865 _Rémy Sigrist_, Jan 16 2023