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A115967 Expansion of 1/(2*sqrt(1-2*x-3*x^2)-1). 3
1, 2, 8, 28, 104, 384, 1428, 5316, 19820, 73948, 276044, 1030796, 3850048, 14382248, 53732172, 200759004, 750134520, 2802980640, 10474015164, 39139487292, 146259311592, 546558514368, 2042458815324, 7632600834924, 28522903136796 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums of number triangle A116392.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

a(n)=sum{k=0..n, A116392(n,k)}.

G.f.: A(x)^2/(2*A(x)-A(x)^2) where A(x) is the g.f. of the central trinomial coefficients A002426.

Also, expansion of (1+2*sqrt(1-2*x-3*x^2))/(3-8*x-12*x^2).

Hankel transform is A000302, A000302(n)=4^n. - Philippe Deléham, Jun 22 2007

G.f.: 1/(2*sqrt(1-2*x-3*x^2)-1)=1/(1 - 2*x/G(0)) ; G(k)=  1 - 2*x/(1 + x/(1 + x/(1 - 2*x/(1 - x/(2 - x/G(k+1)))))); (continued fraction ,6-step ). - Sergei N. Gladkovskii, Feb 27 2012

Conjecture: 3*n*a(n) +(-14*n+9)*a(n-1) +(-5*n+3)*a(n-2) +12*(4*n-9)*a(n-3) +36*(n-3)*a(n-4)=0. - R. J. Mathar, Nov 15 2012

a(n) ~ (1/9 + 2/(9*sqrt(13))) * (4+2*sqrt(13))^n / 3^(n-1). - Vaclav Kotesovec, Feb 08 2014

MATHEMATICA

CoefficientList[ Series[1/(2 Sqrt[1 - 2 x - 3 x^2] - 1), {x, 0, 24}], x] (* Robert G. Wilson v, Feb 28 2012 *)

CROSSREFS

Sequence in context: A056711 A114590 A133592 * A150714 A292668 A122447

Adjacent sequences:  A115964 A115965 A115966 * A115968 A115969 A115970

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Feb 03 2006

EXTENSIONS

Entry revised by N. J. A. Sloane, Apr 10 2006

STATUS

approved

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Last modified October 16 14:35 EDT 2018. Contains 316263 sequences. (Running on oeis4.)