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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 REFERENCES M. Bousquet-MÃ©lou, 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

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