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%I #21 Jun 28 2021 09:23:16
%S 1,2,5,11,24,53,117,258,569,1255,2768,6105,13465,29698,65501,144467,
%T 318632,702765,1549997,3418626,7540017,16630031,36678688,80897393,
%U 178424817,393528322,867954037,1914332891,4222194104,9312342245,20539017381,45300228866
%N Number of one-sided n-step prudent walks, avoiding single west step only, i.e., two or more consecutive west steps are permitted.
%H S. Gao and H. Niederhausen, <a href="http://math.fau.edu/Niederhausen/HTML/Papers/Sequences%20Arising%20From%20Prudent%20Self-Avoiding%20Walks-February%2001-2010.pdf">Sequences Arising From Prudent Self-Avoiding Walks</a>, 2010.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,1).
%F a(n) = A052980(n+1). - _R. J. Mathar_, May 16 2011
%F G.f.: (1+x^2)/(1-2*x-x^3).
%e a(2)=5 since there are 5 such walks: WW, NN, EN, NE, EE.
%o (PARI) my(x='x+O('x^35)); Vec((1+x^2)/(1-2*x-x^3)) \\ _Michel Marcus_, Jun 28 2021
%Y Cf. A110513 (essentially a signed version).
%K nonn,walk
%O 0,2
%A _Shanzhen Gao_, May 11 2011