OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Joseph P. S. Kung and Anna de Mier, Rook and queen paths with boundaries, arXiv:1109.1806 [math.CO], 2011.
J. P. S. Kung and A. de Mier, Catalan lattice paths with rook, bishop and spider steps, Journal of Combinatorial Theory, Series A 120 (2013) 379-389. - From N. J. A. Sloane, Dec 27 2012
FORMULA
G.f.: ((1-t)*(1+t-4*t^2)-(1-t)^2*sqrt(1-12*t+16*t^2))/(2*t*(2 - 3*t)^2). [Kung-de Mier]. - corrected by Vaclav Kotesovec, Sep 07 2012
Apparently 2*n*(n+1)*a(n) -n*(29*n-10)*a(n-1) +19*n*(5*n-7)*a(n-2) -2*n*(58*n-149)*a(n-3) +48*n*(n-4)*a(n-4)=0. - R. J. Mathar, Jul 24 2012
a(n) ~ 5/2*sqrt(246*sqrt(5)-550)/sqrt(Pi) * (6+2*sqrt(5))^n/n^(3/2). - Vaclav Kotesovec, Nov 01 2012
Equivalently, a(n) ~ 5^(5/4) * 2^(2*n) * phi^(2*n - 5) / (sqrt(Pi) * n^(3/2)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Dec 08 2021
MATHEMATICA
Table[SeriesCoefficient[((1-t)*(1+t-4t^2)-(1-t)^2*Sqrt[1-12t+16t^2])/(2t*(2-3t)^2), {t, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 07 2012 *)
PROG
(PARI) x='x+O('x^50); Vec(((1-t)*(1+t-4*t^2)-(1-t)^2*sqrt(1-12*t+16*t^2))/(2*t*(2 - 3*t)^2)) \\ G. C. Greubel, Mar 22 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric Werley, Dec 06 2010
EXTENSIONS
Edited by N. J. A. Sloane, Sep 24 2011
Minor edits by Vaclav Kotesovec, Mar 31 2014
STATUS
approved