OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
D. Merlini, Generating functions for the area below some lattice paths, Discrete Mathematics and Theoretical Computer Science AC, 2003, 217-228.
FORMULA
G.f.: (1-sqrt(1-2*t-3*t^2))/((1-3*t)^2*(1+t)).
D-finite with recurrence: n*(2*n-3)*a(n) = 2*(4*n^2 - 3*n-3)*a(n-1) + 2*(2*n^2 - 12*n +3) *a(n-2) - 6*(n-1)*(4*n-1)*a(n-3) - 9*(n-2)*(2*n-1)*a(n-4). - Vaclav Kotesovec, Oct 24 2012
a(n) ~ 3^(n+1)*n/4*(1-4/(sqrt(3*Pi*n))). - Vaclav Kotesovec, Oct 24 2012
MAPLE
G:=(1-sqrt(1-2*t-3*t^2))/((1-3*t)^2*(1+t)): Gser:=series(G, t=0, 30): seq(coeff(Gser, t^n), n=1..28); # Emeric Deutsch, Dec 16 2004
MATHEMATICA
Rest[CoefficientList[Series[(1-Sqrt[1-2x-3x^2])/((1-3x)^2 (1+x)), {x, 0, 30}], x]] (* Harvey P. Dale, Oct 20 2011 *)
PROG
(PARI) x='x+O('x^66); Vec((1-sqrt(1-2*x-3*x^2))/((1-3*x)^2*(1+x))) \\ Joerg Arndt, May 11 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Donatella Merlini (merlini(AT)dsi.unifi.it), Jun 16 2004
EXTENSIONS
More terms from Emeric Deutsch, Dec 16 2004
STATUS
approved