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%I #17 Jan 11 2024 17:58:58
%S 1,2,4,8,15,28,53,101,192,364,690,1309,2484,4713,8941,16962,32180,
%T 61052,115827,219744,416893,790921,1500520,2846756,5400806,10246297,
%U 19439064,36879393,69966825,132739618,251830868,477768336,906412247,1719626644
%N 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).
%H Lauren K. Williams, <a href="https://doi.org/10.37236/1255">Enumerating up-side self-avoiding walks on integer lattices</a>, Electr. J. Combin. 3, 1996, #R31.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,1).
%F G.f.: (1 + z^2 + z^3)/(1 - 2z + z^2 - z^3 - z^4).
%e 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.
%p 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);
%t LinearRecurrence[{2,-1,1,1},{1,2,4,8},40] (* _Harvey P. Dale_, Jan 11 2024 *)
%Y Cf. A171856.
%K nonn
%O 0,2
%A _Emeric Deutsch_, Mar 31 2010
%E Definition corrected by _Emeric Deutsch_, Apr 01 2010