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 A153462 #19 Jun 02 2025 01:17:08 %S A153462 1,0,1,1,0,1,1,1,0,2,1,1,1,0,4,2,1,1,2,0,7,2,2,1,2,4,0,13,3,2,2,2,4,7, %T A153462 0,24,4,3,2,4,4,7,13,0,44,5,4,3,4,8,7,13,24,0,81,7,5,4,6,8,14,13,24, %U A153462 44,0,149,9,7,5,8,12,14,26,24,44,81,0,274 %N A153462 Triangle read by rows, = A000931(n-k+3) * (A000073 * 0^(n-k)). %C A153462 An eigentriangle by rows, the Padovan sequence convolved with the tribonacci numbers. %C A153462 Sum of n-th row terms = rightmost term of next row. Row sums = the tribonacci numbers, A000073. %F A153462 Triangle read by rows, = A000931(n-k+3) * (A000073 * 0^(n-k)). %F A153462 Equals infinite lower triangular matrices P*M; where P = a matrix with the Padovan sequence in every column starting with offset 3: (1, 0, 1, 1, 1, 2, 2, 3, 4, 5, ...). %F A153462 M = an infinite lower triangular matrix with the tribonacci sequence prefaced with a 1 as the main diagonal: (1, 1, 1, 2, 4, 7, 13, ...) and the rest zeros. %e A153462 First few rows of the triangle = %e A153462 1; %e A153462 0, 1; %e A153462 1, 0, 1; %e A153462 1, 1, 0, 2; %e A153462 1, 1, 1, 0, 4; %e A153462 2, 1, 1, 2, 0, 7; %e A153462 2, 2, 1, 2, 4, 0, 13; %e A153462 3, 2, 2, 2, 4, 7, 0, 24; %e A153462 4, 3, 2, 4, 4, 7, 13, 0, 44; %e A153462 5, 4, 3, 4, 8, 7, 13, 24, 0, 81; %e A153462 7, 5, 4, 6, 8, 14, 13, 24, 44, 0, 149; %e A153462 9, 7, 5, 8, 12, 14, 26, 24, 44, 81, 0, 274; %e A153462 12, 9, 7, 10, 16, 21, 26, 48, 44, 81, 149, 0, 504; %e A153462 ... %e A153462 Row 9 = (2, 2, 1, 2, 4, 0, 13) = termwise products of (1, 1, 1, 2, 4, 7, 13) and (2, 2, 1, 1, 1, 0, 1). Dot product = 24 = A000073(8). %Y A153462 Cf. A000073, A000931. %K A153462 nonn,tabl %O A153462 3,10 %A A153462 _Gary W. Adamson_, Dec 27 2008