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 A251635 #8 Jan 11 2015 08:16:35 %S A251635 1,-2,1,0,-2,1,0,0,-2,1,0,0,0,-2,1,0,0,0,0,-2,1,0,0,0,0,0,-2,1,0,0,0, %T A251635 0,0,0,-2,1,0,0,0,0,0,0,0,-2,1,0,0,0,0,0,0,0,0,-2,1,0,0,0,0,0,0,0,0,0, %U A251635 -2,1,0,0,0,0,0,0,0,0,0,0,-2,1,0,0,0,0,0 %N A251635 Riordan array (1-2*x,x), inverse of Riordan array (1/(1-2*x), x) = A130321. %C A251635 This is a simple Riordan array, an infinite lower triangular matrix. It is the inverse matrix of A130321 (with zeros above the diagonal). %C A251635 Row sums have o.g.f. (1-2*x)/(1-x) and give 1, repeat(-1), i.e., A153881(n+1), n >= 0. %C A251635 Alternate row sums have o.g.f. (1-2*x)/(1+x) and give 1, repeat(-3,3), i.e., (-1)^n*A122553(n). %F A251635 T(n, k) = 0 if n < k and k = 0..(n-2) for n >= 2, and T(n, n) = 1 and T(n, n-1) = -2. %F A251635 G.f. for row polynomials P(n, x) = -2^x^(n-1) + x^n is (1-2*z)/(1-x*z). %F A251635 G.f. for k-th column: (1-2*x)*x^k, k >= 0. %e A251635 The triangle T(n, k) begins: %e A251635 n\k 0 1 2 3 4 5 6 7 8 9 10 ... %e A251635 0: 1 %e A251635 1: -2 1 %e A251635 2: 0 -2 1 %e A251635 3: 0 0 -2 1 %e A251635 4: 0 0 0 -2 1 %e A251635 5: 0 0 0 0 -2 1 %e A251635 6: 0 0 0 0 0 -2 1 %e A251635 7: 0 0 0 0 0 0 -2 1 %e A251635 8: 0 0 0 0 0 0 0 -2 1 %e A251635 9: 0 0 0 0 0 0 0 0 -2 1 %e A251635 10: 0 0 0 0 0 0 0 0 0 -2 1 %e A251635 ... %o A251635 (Haskell) %o A251635 a251635 n k = a251635_tabl !! n !! k %o A251635 a251635_row n = a251635_tabl !! n %o A251635 a251635_tabl = [1] : iterate (0 :) [-2, 1] %o A251635 -- _Reinhard Zumkeller_, Jan 11 2015 %Y A251635 Cf. A130321, A153881, A122553. %K A251635 sign,easy,tabl %O A251635 0,2 %A A251635 _Wolfdieter Lang_, Jan 10 2015