

A191605


Number of nstep twosided prudent selfavoiding walks.


4



1, 4, 10, 26, 66, 168, 426, 1078, 2722, 6862, 17274, 43432, 109086, 273734, 686334, 1719604, 4305666, 10774550, 26948142, 67367456, 168337622, 420472716, 1049866442, 2620488898, 6538734758, 16310909604, 40676600026, 101414764862, 252787228590, 629960214066
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


REFERENCES

M. BousquetMÃ©lou, Families of prudent selfavoiding walks, DMTCS proc. AJ, 2008, 167180.
E. Duchi, On some classes of prudent walks, in: FPSAC'05, Taormina, Italy, 2005.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..750


FORMULA

G.f.: 1/(12*t2*t^2+2*t^3)*(1+tt^3+t*(1t)*sqrt((1t^4)/(12*tt^2))).


EXAMPLE

a(2) = 10: NN, NE, NW, SS, SE, WW, WN, EE, EN, ES.


MAPLE

a:= n> coeff(series(1/(12*t2*t^2+2*t^3) *(1+tt^3+t*(1t) *sqrt((1t^4) /(12*tt^2))), t, n+3), t, n):
seq(a(n), n=0..30);


CROSSREFS

Sequence in context: A285186 A178037 A175658 * A277236 A218208 A207095
Adjacent sequences: A191602 A191603 A191604 * A191606 A191607 A191608


KEYWORD

nonn,walk


AUTHOR

Alois P. Heinz, Jun 08 2011


STATUS

approved



