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 A159934 #11 Feb 10 2022 20:30:23 %S A159934 1,1,1,-1,1,2,0,-1,2,2,-1,0,-2,2,3,2,-1,0,-2,3,2,-1,2,-2,0,-3,2,4,-1, %T A159934 -1,4,-2,0,-2,4,2,3,-1,-2,4,-3,0,-4,2,4,-4,3,-2,-2,6,-2,0,-2,4,3,2,-4, %U A159934 6,-2,-3,4,-4,0,-4,3,4 %N A159934 Triangle, row sums = d(n) = A000005(n): M * Q; where M = an infinite lower Toeplitz matrix with A159933 in every column. Q = an infinite lower triangular matrix with d(n) shifted: (1, 1, 2, 2, 3, 2, 4, ...) as the main diagonal and the rest zeros. %C A159934 Triangle = an infinite lower triangular Toeplitz matrix with the INVERTi transform of d(n) in every column; i.e., A159933: (1, 1, -1, 0, -1, 2, -1, ...). Row sums of the resulting eigentriangle of d(n) = d(n). %C A159934 Sum of n-th row terms = rightmost term of next row. %C A159934 Right border = d(n) shifted. %e A159934 First few rows of the triangle: %e A159934 1; %e A159934 1, 1; %e A159934 -1, 1, 2; %e A159934 0, -1, 2, 2; %e A159934 -1, 0, -2, 2, 3; %e A159934 2, -1, 0, -2, 3, 2; %e A159934 -1, 2, -2, 0, -3, 2, 4; %e A159934 -1, -1, 4, -2, 0, -2, 4, 2; %e A159934 3, -1, -2, 4, -3, 0, -4, 2, 4; %e A159934 -4, 3, -2, -2, 6, -2, 0, -2, 4, 3; %e A159934 2, -4, 6, -2, -3, 4, -4, 0, -4, 3, 4; %e A159934 2, 2, -8, 6, -3, -2, 8, -2, 0, -3, 4, 2; %e A159934 -3, 2, 4, -8, 9, -2, -4, 4, -4, 0, -4, 2, 6; %e A159934 0, -3, 4, 4, -12, 6, -4, -2, 8, -3, 0, -2, 6, 2; %e A159934 0, 0, -6, 4, 6, -8, 12, -2, -4, 6, -4, 0, -6, 2, 4; %e A159934 6, 0, 0, -6, 6, 4, -16, 6, -4, -3, 8, -2, 0, -2, 4, 4; %e A159934 ... %e A159934 Example: row 6 = (2, -1, 0, -2, 3, 2) = termwise products of (2, -1, 0, -1, 1, 1) and (1, 1, 2, 2, 3, 2); with dot product sum = 4 = d(6). %Y A159934 Cf. A000005, A159933. %K A159934 tabl,sign %O A159934 1,6 %A A159934 _Gary W. Adamson_, Apr 26 2009