A116908 - OEIS

A116908

Triangle, read by rows, where row n+1 is formed by sorting, in ascending order, the result of the convolution of row n with {1,2}.

1, 1, 2, 1, 2, 3, 1, 3, 3, 5, 1, 4, 5, 6, 8, 1, 5, 8, 9, 11, 14, 1, 6, 13, 14, 17, 20, 24, 1, 7, 19, 24, 37, 31, 37, 44, 1, 8, 26, 43, 44, 51, 58, 68, 81, 1, 9, 34, 69, 81, 87, 95, 109, 126, 149, 1, 10, 43, 103, 149, 150, 168, 182, 204, 235, 274

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OFFSET

1,3

COMMENTS

See also: A103284 Triangle, read by rows, where row n+1 is formed by sorting, in ascending order, the result of the convolution of row n with {1,1}. Main diagonal is: 1, 2, 3, 5, 8, 14, 24, 44, 81, 149, 274,... This is lexicographically second of an infinite sequence of triangles such as Paul D. Hanna's A103284.

LINKS

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

EXAMPLE

Convolution of row 5 {1,4,5,6,8} with {1,2} = {1,5,9,11,14,8}; sort to obtain row 6: {1,5,8,9,11,14}.

Rows begin:

1,2,

1,2,3,

1,3,3,5,

1,4,5,6,8,

1,5,8,9,11,14,

1,6,13,14,17,20,24,

1,7,19,24,37,31,37,44,