A173302 Irregular triangle by rows, generated from an array with A000041 starting again at columns (2^n - 1), n=1,2,3,...

1, 1, 1, 2, 1, 3, 2, 1, 5, 3, 1, 7, 5, 2, 11, 7, 3, 15, 11, 5, 1, 22, 15, 7, 1, 30, 22, 11, 2, 42, 30, 15, 3, 56, 42, 22, 5, 77, 56, 30, 7, 101, 77, 42, 11, 135, 101, 56, 15, 176, 135, 77, 22, 1, 231, 176, 101, 30, 1, 297, 231, 135, 42, 2

Offset: 0

Author

Gary W. Adamson, Feb 15 2010

Keywords

• nonn
• tabf

Comments

Sum of finite difference terms of the array create triangle A173304.

Row sums = A173303.

Examples

			The generating array =
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176,...
...1, 1, 2, 3, 5,..7,.11, 15, 22, 30, 42, 56, .77, 101, 135,...
.........1, 1, 2,..3...5,..7, 11, 15, 22, 30, .42, .56, .77,...
.......................1,..1,..2,..3,..5,..7,..11,..15,..22,...
..........................................................1,...
...then columns become the rows of triangle A173302:
1;
1, 1;
2, 1;
3, 2, 1;
5, 3, 1;
7, 5, 2;
11, 7, 3;
15, 11, 5, 1;
22, 15, 7, 1;
30, 22, 11, 2;
42, 30, 15, 3;
56, 42, 22, 5;
77, 56, 30, 7;
101, 77, 4, 11;
135, 101, 56, 15;
176, 135, 77, 22, 1;
...
		

Crossrefs

Cf. A000041, A173301, A173303, A173304.

Formula

Create an array with A000041 in row 0, then A000041 starts anew under successive columns (1, 3, 7, 15, 31,...). (Cf. A173301).

Columns of the array = rows of A173302.