A171858 - OEIS

%I #11 Jul 22 2022 08:26:07

%S 1,2,4,9,19,39,79,161,330,678,1392,2855,5853,12000,24607,50463,103487,

%T 212220,435191,892428,1830073,3752882,7695938,15781850,32363392,

%U 66366683,136096274,279088794,572319539,1173639562,2406749561

%N Number of n-step up-side self-avoiding walks on the lattice strip {0,1,2,3} 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_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1,2,1).

%F G.f.: (1+z)(1 - z + z^2 + z^3)/(1 - 2z + z^3 - 2z^4 - z^5).

%e a(3)=9 because we have UUU, UUR, URU, URR, RUU, RUR, RRU, RRR, and RUL, where U, L, and R denote up, left, and right steps, respectively.

%p g := (1+z)*(1-z+z^2+z^3)/(1-2*z+z^3-2*z^4-z^5): gser := series(g, z = 0, 43): seq(coeff(gser, z, n), n = 0 .. 30);

%Y Cf. A171856, A171857.

%K nonn,easy

%O 0,2

%A _Emeric Deutsch_, Mar 31 2010