login
Triangle, rows = inverse binomial transforms of sequences generated from the Pell polynomials.
0

%I #2 Mar 30 2012 17:25:13

%S 1,2,1,5,5,2,12,21,18,6,29,80,116,84,24,70,290,642,774,480,120

%N Triangle, rows = inverse binomial transforms of sequences generated from the Pell polynomials.

%C Columns of A118243 are f(x), the Pell polynomials. (terms of A038137 considered as Pell polynomial coefficients): 1; (x + 1); (x^2 + 2x + 2); (x^3 + 3x^2 + 5x + 3); (x^4 + 4x^3 + 9x^2 + 10x + 5);...For example, (x^3 + 3x^2 + 5x + 3), (f(x), x=1,2,3...), generates column 3 of triangle A118243: (12, 33, 72, 135, 228, 357...); and the inverse binomial transform of (12, 33, 72...) = row 3 of the triangle: (12, 21, 18, 6). The array of A118243 is obtained by deleting the Fibonacci sequence (first row of the A073133 array).

%F n-th row of the triangle = inverse binomial transform of n-th column of A118243.

%e Row 3 of the triangle = (5, 5, 2), = inverse binomial transform of column 3 of A118243: (5, 10, 17, 26, 37...). Example: 17 = 1*2 + 1*5 + 2*5 = 2 + 5 + 10.

%e First few rows of the triangle are:

%e 1;

%e 2, 1;

%e 5, 5, 2;

%e 12, 21, 18, 6;

%e 29, 80, 116, 84, 24;

%e 70, 290, 642, 774, 480, 120;

%e ...

%Y Cf. A038137, A118243, A073133.

%K nonn,tabl

%O 0,2

%A _Gary W. Adamson_, Apr 17 2006