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

0,4

Comments

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

Row sums = A173303.

Links

Table of n, a(n) for n=0..63.

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.

Example

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.

Sequence in context: A002335 A280738 A207375 * A251721 A251722 A304100

Adjacent sequences: A173299 A173300 A173301 * A173303 A173304 A173305

Keyword

nonn,tabf

Author

Gary W. Adamson, Feb 15 2010

Status

approved