

A106396


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


2



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
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OFFSET

1,5


COMMENTS

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


LINKS



FORMULA

nth column (offset) is generated by P * V; P = the Narayana triangle as an infinite lower triangular matrix, V = vector for nth 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;
...


CROSSREFS



KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



