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

0,4

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)

Links

Table of n, a(n) for n=0..54.

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]

Example

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

Crossrefs

Sequence in context: A185416 A193918 A298804 * A108073 A057731 A126074

Adjacent sequences: A155785 A155786 A155787 * A155789 A155790 A155791

Keyword

easy,nonn,tabl

Author

Paul Barry, Jan 27 2009

Status

approved