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 A145462 #9 Jun 02 2025 00:39:19 %S A145462 1,1,1,-1,1,2,0,-1,2,2,1,0,-2,2,3,-1,1,0,-2,3,4,0,-1,2,0,-3,4,5,1,0, %T A145462 -2,2,0,-4,5,7,-1,1,0,-2,3,0,-5,7,9,0,-1,2,0,-3,4,0,-7,9,12,1,0,-2,2, %U A145462 0,-4,5,0,-9,12,16,-1,1,0,-2,3,0,-5,7,0,-12,16,21 %N A145462 Eigentriangle, row sums = the Padovan sequence, A000931. %C A145462 Right border = Padovan sequence starting with offset 6. %C A145462 Row sums = Padovan sequence starting with offset 7. %C A145462 Sum of n-th row terms = rightmost term of next row. %F A145462 Triangle read by rows, T(n,k) = M * (A000931 * 0^(n-k)). M = an infinite lower triangular matrix with A106510 in every column: (1, 1, -1, 0, 1, -1, 0, 1, -1,...); and A000931 is a diagonalized infinite lower triangular matrix with the Padovan sequence starting with offset 6: (1, 1, 2, 2, 3, 4, 5, 7, 9,...) as the main diagonal and the rest zeros. %e A145462 First few rows of the triangle = %e A145462 1; %e A145462 1, 1; %e A145462 -1, 1, 2; %e A145462 0, -1, 2, 2; %e A145462 1, 0, -2, 2, 3; %e A145462 -1, 1, 0, -2, 3, 4; %e A145462 0, -1, 2, 0, -3, 4, 5; %e A145462 1, 0, -2, 2, 0, -4, 5, 7; %e A145462 -1, 1, 0, -2, 3, 0, -5, 7, 9; %e A145462 0, -1, 2, 0, -3, 4, 0, -7, 9, 12; %e A145462 1, 0, -2, 2, 0, -4, 5, 0, -9, 12, 16; %e A145462 ... %e A145462 Example: Row 10 = (1, 0, -2, 2, 3) with A000931(10) = 3, rightmost term. This row = the termwise products of (1, 0, -1, 1, 1) and (1, 1, 2, 2, 3); where the Padovan sequence starting with offset 6 = (1, 1, 2, 2, 3, 4, 5, 7, 9,...). %Y A145462 A000931, A106510 %K A145462 eigen,tabl,sign %O A145462 6,6 %A A145462 _Gary W. Adamson_, Oct 10 2008