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 A118243 #11 Feb 13 2022 23:15:27
%S A118243 1,1,2,1,3,5,1,4,10,12,1,5,17,33,29,1,6,26,72,109,70,1,7,37,135,305,
%T A118243 360,169,1,8,50,228,701,1292,1189,408,1,9,65,357,1405,3640,5473,3927,
%U A118243 985,1,10,82,528,2549,8658,18901,23184,12970,2378,1,11,101,747,4289
%N A118243 Triangle generated from Pell polynomials.
%C A118243 a(k)/a(k-1) of the array sequences tend to exp(arcsinh(N/2)) with rows starting N = 2, 3, 4, .... For example, terms of the Pell sequence row N=2 tend to converge to 2.414... = 1 + sqrt(2).
%C A118243 For scalar s, let V_m(s) be polynomials defined by V_0(s)=1, V_1(s)=s and V_m(s)=s*V_{m-1}(s)+V_{m-2}(s) (m>1). Then the generating array A (not the triangle) in the example below is given identically by the infinite matrix A=(A_{r,c}) with entries A_{r,c}=V_c(r+2); r=0,1,2,...; c=0,1,2,.... - _L. Edson Jeffery_, Aug 14 2011
%F A118243 Triangle, antidiagonals of the array in A073133, deleting the first row (Fibonacci numbers). Columns are generated as f(x) from the Pell polynomials (analogous to the Fibonacci polynomials).
%e A118243 First few rows of the triangle:
%e A118243 1;
%e A118243 1, 2;
%e A118243 1, 3, 5;
%e A118243 1, 4, 10, 12;
%e A118243 1, 5, 17, 33, 29;
%e A118243 1, 6, 26, 72, 109, 70;
%e A118243 ...
%e A118243 Deleting first row of the A073133 array, the generating array of the triangle is
%e A118243 1, 2, 5, 12, 29, ...
%e A118243 1, 3, 10, 33, 109, ...
%e A118243 1, 4, 17, 72, 305, 1292, ...
%e A118243 1, 5, 26, 135, 701, 3640, ...
%e A118243 ...
%e A118243 By rows starting N = 2,3,... the generators of the array are a(k) = N(k-1)+ (k-2) (a generalized Fibonacci operation). Thus row (N=3) = 1, 3, 10, 33, ...
%e A118243 Columns of the array are generated from the terms of A038137 considered as Pell polynomials (analogous to the Fibonacci polynomials):
%e A118243 (1); (x + 1); (x^2 + 2x + 2); (x^3 + 3x^2 + 5x + 3); (x^4 + 4x^3 + 9x^2 + 10x + 5); and so on, where coefficient sums = the Pell numbers (1, 2, 5, 12, 29, ...).
%e A118243 k-th column of the triangle (offset T(0,0)) is generated from f(x), k-th degree Pell polynomial. For example, T(4,3)= 33, = f(2) using x^3 + 3x^2 + 5x + 3 = (8+12+10+3) = 33.
%Y A118243 Cf. A073133, A038137.
%K A118243 nonn,tabl
%O A118243 0,3
%A A118243 _Gary W. Adamson_, Apr 17 2006