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 A179510 #9 Jul 22 2025 08:18:07
%S A179510 0,0,0,1,1,2,3,4,4,5,5,6,7,7,8,9,9,10,10,11,12,13,13,14,15,16,17,17,
%T A179510 18,18,19,19,20,21,22,22,23,23,24,24,25,26,26,27,28,29,30,31,31,32,32,
%U A179510 33,34,34,35,36,36,37,38,39,39,40,41,41,42,42,43,43,44,44,45,45,46,47,47,48,49,49,50,50,51,52,53,53,54,55,56,56,57,57,58,59,60,60,61,62,62,63,64,64,65
%N A179510 Number of equally-spaced triples (x,y,z) of preceding terms with x+y=z.
%C A179510 a(n) is the number of 3-element subsets (i,j,k) of {0,...,n-1} such that k-j=j-i>0 and a(i)+a(j)=a(k). An induction argument can show simultaneously that a(n)-a(n-1) is always 0 or 1 and that the only case where three values of a(n) are equal is a(0)=a(1)=a(2)=0. Numerical evidence suggests that a(n) is asymptotic to 2n/3.
%e A179510 For n=9, just the triples (0,1,2),(2,3,4),(3,4,5),(4,5,6),(4,6,8) satisfy the stated conditions, so a(9) = 5
%Y A179510 A178976 has a somewhat similar definition
%K A179510 nonn,easy
%O A179510 0,6
%A A179510 _Alex Abercrombie_, Jan 08 2011