A161364 Triangle read by rows, modified version of A161363; row sums = A000041

1, 1, 0, 2, 0, 0, 2, 1, 0, 0, 4, 1, 0, 0, 0, 3, 2, 2, 0, 0, 0, 7, 2, 2, 0, 0, 0, 0, 7, 3, 2, 3, 0, 0, 0, 0, 12, 3, 4, 3, 0, 0, 0, 0, 0, 13, 5, 4, 3, 5, 0, 0, 0, 0, 0, 22, 6, 6, 3, 5, 0, 0, 0, 0, 0, 0, 2, 5, 7, 6, 6, 5, 7, 0, 0, 0, 0, 0, 0, 4, 9, 8, 6, 5, 7, 0, 0, 0, 0, 0, 0, 0

Offset

0,4

Comments

Row sums = A000041, the partition numbers.

Links

Table of n, a(n) for n=0..91.

Formula

Given triangle A161363, (the inverse of partition triangle A026794); multiply by (-1), delete right border of 1's, and shift down 1 row inserting a "1" at T(0,0); = triangle M. Let Q = an infinite lower triangular matrix with A000041 as the right border and the rest zeros. Triangle A161364 = M * Q.

Example

First few rows of the triangle =
1;
1, 0;
2, 0, 0;
2, 1, 0, 0;
4, 1, 0, 0, 0;
3, 2, 2, 0, 0, 0;
7, 2, 2, 0, 0, 0, 0;
7, 3, 2, 3, 0, 0, 0, 0;
12, 3, 4, 3, 0, 0, 0, 0, 0;
13, 5, 4, 3, 5, 0, 0, 0, 0, 0;
22, 6, 6, 3, 5, 0, 0, 0, 0, 0, 0;
25, 7, 6, 6, 5, 7, 0, 0, 0, 0, 0, 0;
42, 9, 8, 6, 5, 7, 0, 0, 0, 0, 0, 0, 0;
48, 13, 8, 9, 5, 7, 11, 0, 0, 0, 0, 0, 0, 0;
...

Crossrefs

A161363, A000041

Sequence in context: A365676 A238354 A353836 * A143620 A291529 A366981

Adjacent sequences: A161361 A161362 A161363 * A161365 A161366 A161367

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 07 2009

Status

approved