A204851 Triangle by rows relating to A005773

1, 1, 1, 2, 2, 1, 5, 5, 2, 1, 13, 13, 6, 2, 1, 35, 35, 16, 7, 2, 1, 96, 96, 45, 19, 8, 2, 1, 267, 267, 126, 56, 22, 9, 2, 1, 750, 750, 357, 160, 68, 25, 10, 2, 1, 2123, 2123, 1016, 463, 198, 81, 28, 11, 2, 1, 6046, 6046, 2907, 1337, 586, 240, 95, 31, 12, 2, 1

Offset

0,4

Comments

Left border = A005773. Row sums = A005773 with offset 1

Links

Table of n, a(n) for n=0..65.

Formula

n-th row of the triangle is the top row of M^n, deleting the zeros; where M = the infinite square production matrix:

1, 1, 0, 0, 0, 0, 0,...

1, 1, 1, 0, 0, 0, 0,...

1, 1, 0, 1, 0, 0, 0,...

1, 1, 1, 0, 1, 0, 0,...

1, 1, 1, 1, 0, 1, 0,...

1, 1, 1, 1, 1, 0, 1,...

1, 1, 1, 1, 1, 1, 0,...

...

Example

First few rows of the triangle =
1;
1, 1;
2, 2, 1;
5, 5, 2, 1;
13, 13, 6, 2, 1;
35, 35, 16, 7, 2, 1;
96, 96, 45, 19, 8, 2, 1;
267, 267, 126, 56, 22, 9, 2, 1;
750, 750, 357, 160, 68, 25, 10, 2, 1;
2123, 2123, 1016, 463, 198, 81, 28, 11, 2, 1;
6046, 6046, 2907, 1337, 586, 240, 95, 31, 12, 2, 1;
...
Row 3 = (5, 5, 2, 1) since the top row of M^3 = [5, 5, 2, 1, 0, 0, 0,...]

Crossrefs

Cf. A005773

Sequence in context: A176265 A187307 A280785 * A114292 A333724 A178518

Adjacent sequences: A204848 A204849 A204850 * A204852 A204853 A204854

Keyword

nonn,tabl

Author

Gary W. Adamson, Jan 19 2012

Status

approved