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 A128180 #10 Jul 10 2021 03:02:16 %S A128180 1,-1,2,2,-1,3,-2,3,-1,4,3,-2,4,-1,5,-3,4,-2,5,-1,6,4,-3,5,-2,6,-1,7, %T A128180 -4,5,-3,6,-2,7,-1,8,5,-4,6,-3,7,-2,8,-1,9,-5,6,-4,7,-3,8,-2,9,-1,10 %N A128180 A002260 * A097807. %C A128180 Row sums = A008794: (1, 1, 4, 4, 9, 9, 16, 16, ...). %C A128180 Unsigned row sums = the triangular sequence, A000217: (1, 3, 6, 10, ...) by virtue of the fact that each row is a permutation of the natural numbers. %C A128180 A128179 = A097807 * A002260. %F A128180 A002260 * A097807 as infinite lower triangular matrices. %F A128180 From _Franklin T. Adams-Watters_, Apr 12 2011: (Start) %F A128180 T(n,k) = (2k - 1 + (-1)^(n-k)*(2n+1))/4. %F A128180 |T(n,k)| = (2n+1 + (-1)^(n-k)*(2k-1))/4. (End) %e A128180 Triangle begins: %e A128180 1; %e A128180 -1, 2; %e A128180 2, -1, 3; %e A128180 -2, 3, -1, 4; %e A128180 3, -2, 4, -1, 5; %e A128180 -3, 4, -2, 5, -1, 6; %e A128180 4, -3, 5, -2, 6, -1, 7; %e A128180 ... %o A128180 (PARI) T(n,k)=(2*k-1+(-1)^(n-k)*(2*n+1))/4 \\ _Franklin T. Adams-Watters_, Apr 12 2011 %Y A128180 Cf. A002260, A097807, A008794, A128179. %K A128180 tabl,sign %O A128180 1,3 %A A128180 _Gary W. Adamson_, Feb 17 2007