%I #16 Feb 29 2016 20:19:05
%S 1,2,4,8,16,32,64,126,252,490,980,1890,3780,7252,14504,27734,55468,
%T 105840,211680,403368,806736,1535954,3071908,5845406,11690812,
%U 22238062,44476124,84582428,169164856,321661970,643323940,1223146232,2446292464,4650833040
%N Number of n step walks (each step +/- 1 starting from 0) which are never more than 6 or less than -6.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,7,0,-14,0,7)
%F G.f.: (1 + x - 2*x^2 - x^3)^2/(1 - 7*x^2 + 14*x^4 - 7*x^6).
%t nn=30;r=Solve[{s==1 + x a + x b, a==x s + x c, b==x s +x d, c==x a +x e, d==x b + x f, e==x c+x g, f==x d+x h,g==x e+x i, h==x f+x j,i==x g+x k,j==x h+x l,k==x i,l==x j, z==x k + x l }, {s,a,b,c,d,e,f,g,h,i,j,k,l,z}]; CoefficientList[Series[s+a+b+c+d+e+f+g+h+i+j+k+l/.r,{x,0,nn}],x]
%Y Cf. A068911, A068912, A216212, A216241.
%Y Row n=6 of A068913.
%K nonn,walk,easy
%O 0,2
%A _Geoffrey Critzer_, Jan 14 2014