OFFSET
0,2
COMMENTS
Hankel transform is (-1)^n.
Row sums of the Riordan array ((1-2*x)/(1+x+x^2), x/(1+x+x^2))^(-1). - Paul Barry, Nov 06 2008
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Isaac DeJager, Madeleine Naquin, Frank Seidl, Colored Motzkin Paths of Higher Order, VERUM 2019.
FORMULA
a(n+1) = 3*a(n) + A059738(n) with a(0)=1.
G.f: (sqrt(1-2*x-3*x^2) + 3*(1-3*x))/(2*(2-13*x+21*x^2)). - Paul Barry, Nov 06 2008
Conjecture: +2*n*a(n) -11*n*a(n-1) +4*(2*n+3)*a(n-2) +21*(n-2)*a(n-3)=0. - R. J. Mathar, Nov 24 2012
a(n) ~ 3 * 7^n / 2^(n+1). - Vaclav Kotesovec, Feb 12 2014
MAPLE
seq(coeff(series( (sqrt(1-2*x-3*x^2) + 3*(1-3*x))/(2*(2-13*x+21*x^2)), x, n+1), x, n), n = 0..30); # G. C. Greubel, Jan 29 2020
MATHEMATICA
CoefficientList[Series[(Sqrt[-3*x^2-2*x+1]-3*(3*x-1))/(2*(21*x^2-13*x+2)), {x, 0, 30}], x] (* Vaclav Kotesovec, Feb 12 2014 *)
PROG
(PARI) my(x='x+O('x^30)); Vec( (sqrt(1-2*x-3*x^2) + 3*(1-3*x))/(2*(2-13*x+21*x^2)) ) \\ G. C. Greubel, Jan 29 2020
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (Sqrt(1-2*x-3*x^2) + 3*(1-3*x))/(2*(2-13*x+21*x^2)) )); // G. C. Greubel, Jan 29 2020
(Sage)
def A126932_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (sqrt(1-2*x-3*x^2) + 3*(1-3*x))/(2*(2-13*x+21*x^2)) ).list()
A126932_list(30) # G. C. Greubel, Jan 29 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Philippe Deléham, Mar 17 2007
EXTENSIONS
Corrected and extended by Vincenzo Librandi, Feb 13 2014
STATUS
approved