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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, 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 {} 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 Adjacent sequences: A359862 A359863 A359864 * A359866 A359867 A359868 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.)