A118245 Triangle generated from A001263 considered as a transform.

1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 7, 11, 7, 1, 11, 25, 25, 11, 1, 1, 16, 51, 74, 51, 16, 1, 1, 22, 96, 191, 191, 96, 22, 1, 1, 29, 169, 441, 602, 441, 169, 29, 1

Offset

1,5

Comments

Each row of the triangle is a palindrome.

Links

Table of n, a(n) for n=1..44.

Formula

Let M be the Narayana (or Catalan) triangle, A001263 as an infinite lower triangular matrix. Generate an array by rows, taking the product (M * V); where V = rows of the Narayana triangle considered as vectors. Rows of the triangle are antidiagonals of the array.

Example

First few rows of the array:
  1,  1,  1,   1,   1, ...
  1,  2,  4,   7,  11, ...
  1,  4, 11,  25,  51, ...
  1,  7, 25,  74, 191, ...
  1, 11, 51, 191, 602, ...
  ...
n-th row of the array is generated from (M * V), where V in turn = n-th row of the Narayana triangle: (1); (1, 1); (1, 3, 1); (1, 6, 6, 1); ... i.e., terms followed by zeros to form a vector, as (1, 3, 1, 0, 0, 0, ...). Example: T(6,3) and T(6,4) = 25 = 1*0 + 1*1 + 6*1 + 6*18 = 0+1+6+18 = 25.
First few rows of the triangle:
  1;
  1,  1;
  1,  2,  1;
  1,  4,  4,   1;
  1,  7, 11,   7,   1;
  1, 11, 25,  25,  11,  1;
  1, 16, 51,  74,  51, 16,  1;
  1, 22, 96, 191, 191, 96, 22, 1;
  ...

Crossrefs

Cf. A001263.

Sequence in context: A113582 A347147 A295213 * A104382 A086629 A203948

Adjacent sequences: A118242 A118243 A118244 * A118246 A118247 A118248

Keyword

nonn,tabl

Author

Gary W. Adamson, Apr 17 2006

Status

approved