login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A191605 Number of n-step two-sided prudent self-avoiding 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. Bousquet-Mélou, Families of prudent self-avoiding walks, DMTCS proc. AJ, 2008, 167-180.

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/(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))).

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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 19 00:03 EST 2021. Contains 340262 sequences. (Running on oeis4.)