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 A384450 #21 Jun 13 2025 17:25:57 %S A384450 0,0,0,1,0,1,0,2,0,4,0,5,0,8,0,9,0,12,1,0,1,0,0,5,0,5,0,5,1,0,3,0,3,0, %T A384450 4,0,2,2,2,2,3,0,3,0,2,1,0,7,0,5,0,5,0,7,0,10,1,1,2,1,1,0,9,0,6,3,0,6, %U A384450 1,0,6,3,3,1,2,2,3,0,7,0,6,3,1,0,4,4 %N A384450 a(1) = 0; thereafter, a(n) is the number of arithmetic progressions of length 3 or greater at indices in an arithmetic progression ending at a(n-1). %C A384450 In other words, take the longest arithmetic progression at indices with common difference k ending at a(n-1) and call that length j. a(n) is the sum of each j-2 that corresponds to a distinct common difference k. This means that an arithmetic progression of length 3 is worth 1 point, length 4 is worth 2 points, and so on. %H A384450 Neal Gersh Tolunsky, <a href="/A384450/b384450.txt">Table of n, a(n) for n = 1..10000</a> %e A384450 To find a(10), we see that there are 4 arithmetic progressions ending in a(9) = 0. These occur at indices i = 5,7,9; i = 3,5,7,9; i = 1,3,5,7,9; and i = 1,5,9. So a(10) = 4. %Y A384450 Cf. A308638, A362881. %K A384450 nonn %O A384450 1,8 %A A384450 _Neal Gersh Tolunsky_, May 27 2025 %E A384450 a(32)-a(86) from _Pontus von Brömssen_, May 30 2025