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 A334821 #29 Feb 24 2021 08:22:00 %S A334821 1,2,4,6,10,13,17,22,28,34,41,48,56,64,71,78,90,102,111,124,135,147, %T A334821 160,172,187,201,215,230,246,261,276,294,313,330,350,370,389,412,433, %U A334821 452,475,497,520,543,565,587,612,636,661,690,714,740,768,795,821,850,878,908,942,971,1000,1032,1065 %N A334821 Number of integers from 0 to the triangular number A000217(n) that can be represented as a difference of triangular numbers from 0 to n. %F A334821 a(n) = A000217(n) - A333601(n) + 1. %e A334821 a(2) = 4 as all four numbers from 0 to A000217(2) = 3 can all be represented as a difference of 0,1,3, the triangular numbers from 0 to 2. %e A334821 a(3) = 6 as in the seven numbers from 0 to A000217(3) = 6, six can be represented as a difference of 0,1,3,6, the triangular numbers from 0 to 3. One number, 4, cannot be. %e A334821 a(6) = 17 as in the twenty-two numbers from 0 to A000217(6) = 21, seventeen can be represented as a difference of 0,1,3,6,10,15,21, the triangular numbers from 0 to 6. Five numbers, 8,13,16,17,19, cannot be. %Y A334821 Cf. A333601, A234813, A000217, A001227. %K A334821 nonn %O A334821 0,2 %A A334821 _Scott R. Shannon_, Jun 09 2020