A117935 - OEIS

%I #11 Feb 13 2022 23:15:51

%S 1,1,1,1,2,1,1,2,3,1,1,2,5,4,1,1,2,5,10,5,1,1,2,5,12,17,6,1,1,2,5,12,

%T 25,26,7,1,1,2,5,12,29,46,37,8,1,1,2,5,12,29,66,77,50,9,1,1,2,5,12,29,

%U 70,137,120,65,10,1

%N Triangle, row terms converge to the Pell sequence.

%F Antidiagonals of an array formed by taking binomial transforms of (1,0,0,0,...); (1,1,0,0,0,...); (1,1,2,0,0,0,...); where (1,1,2,2,4,4...) = A016116, the inverse binomial transform of the Pell sequence, A000129, starting 1,2,5,12,...

%e First few rows of the array:

%e   1, 1, 1,  1,  1, ...

%e   1, 2, 3,  4,  5, ...

%e   1, 2, 5, 10, 17, ...

%e   1, 2, 5, 12, 25, ...

%e   1, 2, 5, 12, 29, ...

%e   ...

%e For example, (1, 2, 5, 10, 17, 26, 37, ...) = the binomial transform of (1, 1, 2, 0, 0, 0, ...).

%e First few rows of the triangle:

%e   1;

%e   1, 1;

%e   1, 2, 1;

%e   1, 2, 3,  1;

%e   1, 2, 5,  4,  1;

%e   1, 2, 5, 10,  5,  1;

%e   1, 2, 5, 12, 17,  6, 1;

%e   1, 2, 5, 12, 25, 26, 7, 1;

%e   ...

%Y Cf. A000129, A016116.

%K nonn,tabl

%O 1,5

%A _Gary W. Adamson_, Apr 03 2006