OFFSET
0,2
COMMENTS
For n=2 we have 10 paths: H(1)H(1), H(1)H(2), H(2)H(1), H(2)H(2), H(1)H(3), H(3)H(1), H(3)H(3), H(2)H(3), H(3)H(2), UD.
LINKS
Robert Israel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: 1/(1-3*x-x*F(x)), where F(x) is the g.f. of the sequence A117641.
G.f.: 2*(3+x)/(6-17*x-9*x^2+x*sqrt(1-6*x+5*x^2)).
a(n) ~ 5^(n+3/2)/(98*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Apr 21 2015
From Robert Israel, Apr 28 2015 (Start):
G.f.: (6-x*sqrt(1-6*x+5*x^2)-17*x-9*x^2)/(6-36*x+42*x^2+38*x^3).
3*(-n+1)*a(n) +9*(4*n-7)*a(n-1) +9*(-16*n+39)*a(n-2) +(197*n-656)*a(n-3) +9*(n+15)*a(n-4) +95*(-n+4)*a(n-5)=0. (End)
MAPLE
rec:= (95+95*n)*a(n)+(-180-9*n)*a(n+1)+(-329-197*n)*a(n+2)+(369+144*n)*a(n+3)+(-117-36*n)*a(4+n)+(12+3*n)*a(n+5):
f:= gfun:-rectoproc({rec, a(0)=1, a(1)=3, a(2)=10, a(3)=33, a(4)=110}, a(n), remember):
seq(f(n), n=0..100); # Robert Israel, Apr 28 2015
MATHEMATICA
CoefficientList[Series[2*(3+x)/(6-17*x-9*x^2+x*Sqrt[1-6*x+5*x^2]), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 21 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
José Luis Ramírez Ramírez, Apr 20 2015
STATUS
approved