OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..750
Mireille Bousquet-Mélou, Families of prudent self-avoiding walks, DMTCS proc. AJ, 2008, 167-180.
Nathan Clisby, Enumerative Combinatorics of Lattice Polymers, Notices AMS, 68:4 (April 2021), 504-515. See P_2(x) on page 511, but beware, the denominator has a typo.
Enrica Duchi, On some classes of prudent walks, in: FPSAC'05, Taormina, Italy, 2005.
FORMULA
G.f.: (1/(1-2*t-2*t^2+2*t^3))*(1+t-t^3+t*(1-t)*sqrt((1-t^4)/(1-2*t-t^2))). [Clarified by N. J. A. Sloane, Mar 15 2021]
EXAMPLE
a(2) = 10: NN, NE, NW, SS, SE, WW, WN, EE, EN, ES.
MAPLE
a:= n-> coeff(series((1/(1-2*t-2*t^2+2*t^3)) *(1+t-t^3+t*(1-t) *sqrt((1-t^4) /(1-2*t-t^2))), t, n+3), t, n):
seq(a(n), n=0..30);
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Alois P. Heinz, Jun 08 2011
STATUS
approved