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 A245557 #21 Aug 05 2014 13:34:39 %S A245557 1,3,6,4,3,6,15,12,7,3,6,9,24,21,18,10,3,6,9,12,33,30,27,24,13,3,6,9, %T A245557 12,15,42,39,36,33,30,16,3,6,9,12,15,18,51,48,45,42,39,36,19,3,6,9,12, %U A245557 15,18,21,60,57,54,51,48,45,42,22 %N A245557 Irregular triangle read by rows: T(n,k) (n>=0, 0 <= k <= 2n) = number of triples (u,v,w) with entries in the range 0 to n which have some pair adding up to k and in which at least one of u,v,w is equal to n. %C A245557 The sum of (left-justified) rows 0 through n gives row n of A245556. For example, the sum of rows 0 thru 2 is 7, 12, 19, 12, 7, which is the n=2 row of A245556. %F A245557 T(n,k) = 3k (0 <= k <= n-1), T(n,k) = 12n-3k-3 (n <= k <= 2n-1), T(n,2n) = 3n+1. %e A245557 Triangle begins: %e A245557 [1] %e A245557 [3, 6, 4] %e A245557 [3, 6, 15, 12, 7] %e A245557 [3, 6, 9, 24, 21, 18, 10] %e A245557 [3, 6, 9, 12, 33, 30, 27, 24, 13] %e A245557 [3, 6, 9, 12, 15, 42, 39, 36, 33, 30, 16] %e A245557 [3, 6, 9, 12, 15, 18, 51, 48, 45, 42, 39, 36, 19] %e A245557 [3, 6, 9, 12, 15, 18, 21, 60, 57, 54, 51, 48, 45, 42, 22] %e A245557 ... %e A245557 Example. Suppose n = 2. We find: %e A245557 triple count pair-sums 0 1 2 3 4 %e A245557 ------------- %e A245557 002 3 0,2 3 3 %e A245557 012 6 1,2,3 6 6 6 %e A245557 112 3 2,3 3 3 %e A245557 022 3 2,4 3 3 %e A245557 122 3 3,4 3 3 %e A245557 222 1 4 1 %e A245557 ------------- %e A245557 Totals: 3 6 15 12 7, which is row 2 of the triangle. %p A245557 See A245556. %Y A245557 Partial sums of the rows gives A245556. %Y A245557 Row sums are A082040. %K A245557 nonn,tabf %O A245557 0,2 %A A245557 _N. J. A. Sloane_, Aug 04 2014