A117935 Triangle, row terms converge to the Pell sequence.

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, 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, 70, 137, 120, 65, 10, 1

Offset

1,5

Links

Table of n, a(n) for n=1..66.

Formula

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,...

Example

First few rows of the array:
  1, 1, 1,  1,  1, ...
  1, 2, 3,  4,  5, ...
  1, 2, 5, 10, 17, ...
  1, 2, 5, 12, 25, ...
  1, 2, 5, 12, 29, ...
  ...
For example, (1, 2, 5, 10, 17, 26, 37, ...) = the binomial transform of (1, 1, 2, 0, 0, 0, ...).
First few rows of the triangle:
  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, 25, 26, 7, 1;
  ...

Crossrefs

Cf. A000129, A016116.

Sequence in context: A259799 A208447 A320750 * A224698 A179749 A103462

Adjacent sequences: A117932 A117933 A117934 * A117936 A117937 A117938

Keyword

nonn,tabl

Author

Gary W. Adamson, Apr 03 2006

Status

approved