OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
From Vaclav Kotesovec, Oct 24 2012: (Start)
G.f.: (3 - 6*x + sqrt(-1 + 4*x*(9*x-11) + 4*sqrt(1-x)*sqrt(5+4*x)*sqrt(9*x-1))) / (sqrt(10+8*x)*sqrt((1-x)*(1-9*x))*(4*x*(9*x-11)-1+4*sqrt(1-x)*sqrt(5+4*x)*sqrt(9*x-1))^(1/4))
D-finite with recurrence: 15*(n-1)*n*a(n) = (n-1)*(133*n-54)*a(n-1) + (31*n^2 - 177*n + 224)*a(n-2) - (113*n^2 - 295*n + 144)*a(n-3) - 18*(n-3)*(2*n-5)*a(n-4)
a(n) ~ 3^(2*n+3/2)/(2*sqrt(14*Pi*n))
(End)
a(n) = A091533(2*n,n) for n >= 0. - Paul D. Hanna, Dec 11 2018
a(n) = [x^n*y^n] 1/(1 - x - y - x^2 - x*y - y^2) for n >= 0. - Paul D. Hanna, Dec 11 2018
MATHEMATICA
FullSimplify[CoefficientList[Series[(3-6*x+Sqrt[-1+4*x*(9*x-11)+4*Sqrt[1-x]*Sqrt[5+4*x]*Sqrt[9*x-1]])/(Sqrt[10+8*x]*Sqrt[(1-x)*(1-9*x)]*(4*x*(9*x-11)-1+4*Sqrt[1-x]*Sqrt[5+4*x]*Sqrt[9*x-1])^(1/4)), {x, 0, 10}], x]]
PROG
(PARI) /* same as in A092566 but use */
steps=[[0, 1], [0, 2], [1, 0], [2, 0], [1, 1]];
/* Joerg Arndt, Jun 30 2011 */
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Eric Werley, Jun 29 2011
EXTENSIONS
Terms > 425712429 by Joerg Arndt, Jun 30 2011
STATUS
approved