cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Gary W. Adamson, May 01 2005

Keywords

Comments

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

Examples

			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

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, ...]).

Extensions

More terms from Alois P. Heinz, Nov 28 2021