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 A214859 #17 Sep 22 2023 17:32:18 %S A214859 0,1,0,4,3,1,9,8,6,3,16,15,13,10,6,1,25,24,22,19,15,10,4,36,35,33,30, %T A214859 26,21,15,8,0,49,48,46,43,39,34,28,21,13,4,64,63,61,58,54,49,43,36,28, %U A214859 19,9,81,80,78,75,71,66,60,53,45,36,26,15,3,100,99,97 %N A214859 Triangle read by rows, T(n,k) = n^2 - k*(k+1)/2 if k*(k+1)/2 <= n^2. %C A214859 Row lengths are in A214857. %H A214859 Alois P. Heinz, <a href="/A214859/b214859.txt">Rows n = 0..200, flattened</a> %F A214859 T(2*n,n) = A022264(n). %F A214859 T(n,n) = n*(n-1)/2 = A000217(n-1). %e A214859 Triangle begins: %e A214859 0; %e A214859 1, 0; %e A214859 4, 3, 1; %e A214859 9, 8, 6, 3; %e A214859 16, 15, 13, 10, 6, 1; %e A214859 25, 24, 22, 19, 15, 10, 4; %e A214859 36, 35, 33, 30, 26, 21, 15, 8, 0; %e A214859 49, 48, 46, 43, 39, 34, 28, 21, 13, 4; %e A214859 64, 63, 61, 58, 54, 49, 43, 36, 28, 19, 9; %e A214859 81, 80, 78, 75, 71, 66, 60, 53, 45, 36, 26, 15, 3; %e A214859 100, 99, 97, 94, 90, 85, 79, 72, 64, 55, 45, 34, 22, 9; %e A214859 121, 120, 118, 115, 111, 106, 100, 93, 85, 76, 66, 55, 43, 30, 16, 1; %e A214859 ... %t A214859 Table[s = {}; k = 0; While[tri = k*(k + 1)/2; tri <= n^2, AppendTo[s, n^2 - tri]; k++]; s, {n, 0, 10}] (* _T. D. Noe_, Mar 11 2013 *) %Y A214859 Cf. Diagonals: A000217, A034856, A055999, %Y A214859 Columns: A000290, A005563, A028872, A028878. %K A214859 nonn,easy,tabf %O A214859 0,4 %A A214859 _Philippe Deléham_, Mar 09 2013