0,2

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).

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

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.

First few rows of the triangle are:

1;

2, 1;

5, 5, 2;

12, 21, 18, 6;

29, 80, 116, 84, 24;

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

...

Cf. A038137, A118243, A073133.

Sequence in context: A137597 A059340 A046757 this_sequence A108410 A058116 A058118

Adjacent sequences: A118241 A118242 A118243 this_sequence A118245 A118246 A118247

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 17 2006