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 A171857 Number of n-step up-side self-avoiding walks on the lattice strip {0,1,2} x Z (up-side means that the walks move up and sideways but not down). 1
 1, 2, 4, 8, 15, 28, 53, 101, 192, 364, 690, 1309, 2484, 4713, 8941, 16962, 32180, 61052, 115827, 219744, 416893, 790921, 1500520, 2846756, 5400806, 10246297, 19439064, 36879393, 69966825, 132739618, 251830868, 477768336, 906412247, 1719626644 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..33. Lauren K. Williams, Enumerating up-side self-avoiding walks on integer lattices, Electr. J. Combin. 3, 1996, #R31. Index entries for linear recurrences with constant coefficients, signature (2,-1,1,1). FORMULA G.f.: (1 + z^2 + z^3)/(1 - 2z + z^2 - z^3 - z^4). EXAMPLE a(3)=8 because we have UUU, UUR, URU, RUU, RUL, RRU, RUR, and URR, where U, L, and R denote up, left, and right steps, respectively. MAPLE g := (1+z^2+z^3)/(1-2*z+z^2-z^3-z^4): gser := series(g, z = 0, 43): seq(coeff(gser, z, n), n = 0 .. 35); CROSSREFS Cf. A171856. Sequence in context: A239554 A268393 A118870 * A190160 A332052 A088532 Adjacent sequences: A171854 A171855 A171856 * A171858 A171859 A171860 KEYWORD nonn AUTHOR Emeric Deutsch, Mar 31 2010 EXTENSIONS Definition corrected by Emeric Deutsch, Apr 01 2010 STATUS approved

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Last modified June 3 03:20 EDT 2023. Contains 363103 sequences. (Running on oeis4.)