A106396 Triangle read by rows, generated from the Narayana triangle as a matrix.

1, 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 7, 5, 2, 1, 1, 11, 13, 5, 2, 1, 1, 16, 31, 14, 5, 2, 1, 1, 22, 66, 41, 14, 5, 2, 1, 1, 29, 127, 116, 42, 14, 5, 2, 1, 1, 37, 225, 302, 131, 42, 14, 5, 2, 1, 1, 46, 373, 715, 407, 132, 42, 14, 5, 2, 1, 1, 56, 586, 1549, 1205, 428, 132, 42, 14, 5, 2, 1

Offset

1,5

Comments

The n-th column starting from the top has the first n terms in the Catalan sequence: (1, 2, 5, 14, ...)

Links

Table of n, a(n) for n=1..78.

Formula

n-th column (offset) is generated by P * V; P = the Narayana triangle as an infinite lower triangular matrix, V = vector for n-th column comprising n leading 1's and the rest zeros (e.g., V for 3rd column = [1, 1, 1, 0, 0, 0, ...]).

Example

Col. 2 offset = 1, 2, 4, 7, 11, 16, 22, ... since P * [1, 1, 0, 0, 0, ...] = 1, 2, 4, 7, 11, ...
First few rows of the triangle are:
  1;
  1,  1;
  1,  2,  1;
  1,  4,  2,  1;
  1,  7,  5,  2,  1;
  1, 11, 13,  5,  2,  1;
  1, 16, 31, 14,  5,  2,  1;
  ...
Second column = A000124.

Crossrefs

Cf. A000108, A000124, A001263, A137940.

Sequence in context: A124022 A098063 A209438 * A282869 A140998 A048004

Adjacent sequences: A106393 A106394 A106395 * A106397 A106398 A106399

Keyword

nonn,tabl

Author

Gary W. Adamson, May 01 2005

Extensions

More terms from Alois P. Heinz, Nov 28 2021

Status

approved