A155788 Renewal array for 1/(x+sqrt(1-4x)).

1, 1, 1, 3, 2, 1, 9, 7, 3, 1, 29, 24, 12, 4, 1, 97, 85, 46, 18, 5, 1, 333, 306, 177, 76, 25, 6, 1, 1165, 1115, 681, 315, 115, 33, 7, 1, 4135, 4100, 2622, 1288, 510, 164, 42, 8, 1, 14845, 15185, 10104, 5220, 2206, 774, 224, 52, 9, 1

Offset: 0

Author

Paul Barry, Jan 27 2009

Keywords

• easy
• nonn
• tabl

Comments

First column is A081696. Row sums are A000984.

Contribution from Paul Barry, Jan 27 2009: (Start)

First column of A155788.

In general, the image of the sequence with g.f. 1/(1-ax-bx^2) under (1,xc(x)) has g.f.

1/(1-ax-(a+b)x/(1-2x-x^2/(1-2x-x^2/(1-2x-x^2/(1-..... (continued fraction). (End)

Examples

			Triangle begins
1,
1, 1,
3, 2, 1,
9, 7, 3, 1,
29, 24, 12, 4, 1,
97, 85, 46, 18, 5, 1,
333, 306, 177, 76, 25, 6, 1
		

Formula

Riordan array (1/(x+sqrt(1-4x)),x/(x+sqrt(1-4x));

G.f.: 1/(1-x-xy-2x^2/(1-2x-x^2/(1-2x-x^2/(1-2x-x^2/(1-..... (continued fraction).

G.f: 1/(1-x-2x^2/(1-2x-x^2/(1-2x-x^2/(1-2x-x^2/(1-.... (continued fraction). [From Paul Barry, Jan 27 2009]