OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..400
FORMULA
a(0)=1, a(n) = Sum_{d|n} (2*hypergeom([-d+2, d+1], [2], -1))^(n/d) = Sum_{d|n} A006318(d-1)^(n/d) for n >=1.
EXAMPLE
For n=2 the 3 paths are UUDD, UFD, and UDUDUD.
MAPLE
b:= n-> coeff(series((1-x-(1-6*x+x^2)^(1/2))/(2*x), x, n+3), x, n):
a:= n-> `if`(n=0, 1, add(b(d-1)^(n/d), d=numtheory[divisors](n))):
seq(a(n), n=0..30); # Alois P. Heinz, Sep 13 2012
MATHEMATICA
Table[If[n == 0, 1, Sum[(2*Hypergeometric2F1[-d + 2, d + 1, 2, -1])^(n/d), {d, Divisors[n]}]], {n, 0, 26}]
CROSSREFS
KEYWORD
nonn
AUTHOR
David Scambler, Sep 13 2012
STATUS
approved