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Walks of length n on the x-axis using steps {1,0,-1} and visiting no point more than twice.
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%I #9 Oct 27 2017 17:41:20

%S 1,4,12,30,66,148,316,682,1438,3052,6428,13574,28594,60284,127004,

%T 267634,563870,1188084,2503180,5274062,11112002,23412164,49327516,

%U 103929178,218970366,461352988,972033500,2047996278,4314962930,9091278956,19154591420,40357179234

%N Walks of length n on the x-axis using steps {1,0,-1} and visiting no point more than twice.

%C Note: a 0 step counts as a visit and a step but does not contribute to the length of the walk.

%F G.f. (-1-2*x-2*x^2-2*x^3+2*x^4-2*x^5-2*x^6-2*x^7+3*x^8) / ((-1+x^2)^2 * (-1+2*x+x^4)).

%t CoefficientList[Series[ (-1-2*x-2*x^2-2*x^3+2*x^4-2*x^5-2*x^6 -2*x^7+3*x^8)/((-1+x^2)^2 * (-1+2*x+x^4)), {x, 0, 45}], x]

%Y Cf. A212584, A212585, A212586, A164392, A212589.

%K nonn,walk

%O 0,2

%A _David Scambler_, May 22 2012