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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

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

Sequence in context: A285186 A178037 A175658 * A277236 A218208 A207095

Adjacent sequences:  A191602 A191603 A191604 * A191606 A191607 A191608

KEYWORD

nonn,walk,changed

AUTHOR

Alois P. Heinz, Jun 08 2011

STATUS

approved

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Last modified May 13 19:36 EDT 2021. Contains 343868 sequences. (Running on oeis4.)