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

Offset: 1

Author

Jonathan Vos Post, Mar 16 2006

Keywords

• easy
• nonn
• tabl

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.

Examples

			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,
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,...
		

Crossrefs

Cf. A103284.