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 A174026 #6 Feb 08 2022 22:44:10 %S A174026 1,2,1,0,2,4,2,0,1,2,1,0,0,0,0,0,2,4,2,0,4,8,4,0,2,4,2,0,0,0,0,0,1,2, %T A174026 1,0,2,4,2,0,1,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,4,2,0, %U A174026 4,8,4,0,2,4,2,0,0,0,0,0,4,8,4,0,8,16,8,0,4,8,4,0,0,0,0,0,2,4 %N A174026 Convolved with its aerated variant = (1, 2, 3, ...). %C A174026 Equals left border of triangle A174064. %C A174026 With suitable polcoeff offsets, we obtain: (x * 2x^2 + x^3 + 2x^5) * (1 + 2x^2 + 4x^4 + 2x^8 + 4x^10 + ...) = (x + 2x^2 + 3x^3 + 4x^4 + 5x^5 + ...). %F A174026 Left border of a multiplication table with columns >1 shifted down twice, with row sums = (1, 2, 3, ...); as shown in triangle A174064. %e A174026 First few rows of triangle A174064 = 1, 2, 1, 0, 2, 4, ... = heading terms, multiplied * left border. %e A174026 1; %e A174026 2, %e A174026 1, 2; %e A174026 0, 4; %e A174026 2, 2, 1; %e A174026 4, 0, 2; %e A174026 2, 4, 1, 0; %e A174026 0, 8, 0, 0; %e A174026 1, 4, 2, 0, 2; %e A174026 2, 0, 4, 0, 4; %e A174026 ... %e A174026 where each successive column > 1 is shifted down twice, with terms filled in as a product of (1, 2, 1, 0, 2, 4, 2, ...) * (1, 2, 1, 0, 2, 4, 2, ...). %e A174026 The next term in the series is generated in the ongoing left column, such that leftmost term = (n - sum of row n terms in columns > 1). %e A174026 For example, a(9) = 1 since the terms to the right of the 1 in row 9 are (4, 2, 0, 2), sum = 8. %Y A174026 Cf. A174064. %K A174026 nonn %O A174026 1,2 %A A174026 _Gary W. Adamson_, Mar 06 2010 %E A174026 More terms from _R. J. Mathar_, Mar 18 2010