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 A342824 #7 Mar 28 2021 00:19:16 %S A342824 1,1,2,1,2,1,2,2,2,1,2,1,2,1,3,1,2,2,2,1,2,1,2,2,2,1,2,1,2,1,2,2,2,1, %T A342824 3,1,2,1,2,1,2,1,3,1,2,1,2,2,2,2,2,1,2,1,2,1,2,1,2,1,2,1,3,1,2,1,2,1, %U A342824 2,1,2,2,2,1,2,1,2,1,2,2,2,1,2,2,2,1,2 %N A342824 Number of ways n appears as a cross-polytope number (A142978). %C A342824 Every entry in the first column (of A142978) is 1, so this sequence starts at a(2). %C A342824 a(n) is always positive, as the first row lists the positive integers. %C A342824 a(n) >= 3 infinitely often. This happens, in particular, at every even square > 4. (The second row contains the squares, and the second column the positive even numbers.) %C A342824 For n <= 10000, the only instance of a(n) > 3 is a(1156) = 4. This occurs because 1156 is even, square, and octahedral (third row of A142978). %o A342824 (Sage) def a(n) : return len([K for K in [2..n] if n == next(A142978(N, K) for N in (1..) if A142978(N, K) >= n)]) %Y A342824 Cf. A142978. %K A342824 nonn %O A342824 2,3 %A A342824 _Eric M. Schmidt_, Mar 22 2021