OFFSET
0,2
LINKS
Robert Israel, Table of n, a(n) for n = 0..500
R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6.
FORMULA
a(n) = sum_j[C(n, j)B(j)B(j+1)B(n-j)] where B(k)=C(k, [k/2])=A001405(k)
E.g.f.: (BesselI(0, 2*x)+BesselI(1, 2*x))^3. - Vladeta Jovovic, Apr 28 2003
From Vaclav Kotesovec, Jun 10 2019: (Start)
Recurrence: (n+1)*(n+2)*(n+3)*a(n) = 4*(5*n^2+10*n+3)*a(n-1) + 4*(n-1)*(10*n^2+10*n-9)*a(n-2) - 144*(n-2)*(n-1)*a(n-3) - 144*(n-3)*(n-2)*(n-1)*a(n-4).
a(n) ~ 6^(n + 3/2) / (Pi*n)^(3/2). (End)
EXAMPLE
a(2)=12 since a(1) is obviously 3 and from each of these three positions there are four possible steps which remain in the first octant.
MAPLE
S:= series((BesselI(0, 2*x)+BesselI(1, 2*x))^3, x, 101):
seq(simplify(coeff(S, x, n))*n!, n=0..100); # Robert Israel, Oct 10 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Aug 23 2001
STATUS
approved