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 A131422 #8 Apr 01 2019 02:43:05 %S A131422 1,3,5,6,8,11,10,12,15,19,15,17,20,24,29,21,23,26,30,35,41,28,30,33, %T A131422 37,42,48,55,36,38,41,45,50,56,63,71,45,47,50,54,59,65,72,80,89,55,57, %U A131422 60,64,69,75,82,90,99,109 %N A131422 (A000012 * A127773) + (A127773 * A000012) - A000012. %C A131422 Left border = the triangular series, A000217. Right border = A028387, (1, 5, 11, 19, 29, 41, 55, 71, ...). Row sums = A131423: (1, 8, 25, 56, 105, 176, 273, ...). %F A131422 (A000012 * A127773) + (A127773 * A000012) - A000012 as infinite lower triangular matrices. %F A131422 T(n,k) = (n^2 + n + k^2 + k - 2)/2 (1 <= k <= n). - _Emeric Deutsch_, Sep 06 2008 %e A131422 First few rows of the triangle are: %e A131422 1; %e A131422 3, 5; %e A131422 6, 8, 11; %e A131422 10, 12, 15, 19; %e A131422 15, 17, 20, 24, 29; %e A131422 21, 23, 26, 30, 35, 41; %e A131422 28, 30, 33, 37, 42, 48, 55; %e A131422 ... %p A131422 T:=proc(n,k) options operator, arrow: (1/2)*n*(n+1)+(1/2)*k*(k+1)-1 end proc: for n to 10 do seq(T(n,k),k=1..n) end do; # yields sequence in triangular form - _Emeric Deutsch_, Sep 06 2008 %Y A131422 Cf. A127773, A000217, A028387, A131423. %K A131422 nonn,tabl %O A131422 1,2 %A A131422 _Gary W. Adamson_, Jul 10 2007