Search: id:A118243
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%I A118243
%S A118243 1,1,2,1,3,5,1,4,10,12,1,5,17,33,29,1,6,26,72,109,70,1,7,37,135,305,360,
%T A118243 169,1,8,50,228,701,1292,1189,408,1,9,65,357,1405,3640,5473,3927,985,1,
%U A118243 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)).
%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 are:
%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.
%Y A118243 Sequence in context: A047997 A049069 A030237 this_sequence A134081 A134247 
               A153277
%Y A118243 Adjacent sequences: A118240 A118241 A118242 this_sequence A118244 A118245 
               A118246
%K A118243 nonn,tabl
%O A118243 0,3
%A A118243 Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 17 2006

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