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Number of n-step walks (each step +-1 starting from 0) which are never more than 5 or less than -5.
3

%I #31 May 19 2019 20:35:23

%S 1,2,4,8,16,32,62,124,236,472,890,1780,3340,6680,12502,25004,46732,

%T 93464,174554,349108,651740,1303480,2432918,4865836,9080956,18161912,

%U 33892954,67785908,126494956,252989912,472095062,944190124,1761901676,3523803352,6575544410,13151088820

%N Number of n-step walks (each step +-1 starting from 0) which are never more than 5 or less than -5.

%F a(n) = A068913(5,n).

%F a(n) = 6*a(n-2) - 9*a(n-4) + 2*a(n-6).

%F a(n) = 2^n for n < 6.

%F G.f.: ((1-x)^2*(1+x)^2*(1+2*x)) / ((1-2*x^2)*(1-4*x^2+x^4)).

%F a(2*n+1) = 2*a(2*n).

%F a(n) = Sum_{k=0..n} A214846(n-k, k). - _Philippe Deléham_, Mar 25 2013

%t nn=35;CoefficientList[Series[(1+2x)(1-x^2)^2/(1-6x^2+9x^4-2x^6),{x,0,nn}],x] (* _Geoffrey Critzer_, Jan 14 2014 *)

%Y Cf. Rows of A068913: A000007, A016116 (without initial term), A068911, A068912, A214846, A216212.

%K nonn,walk,easy

%O 0,2

%A _Philippe Deléham_, Mar 15 2013

%E a(34) corrected by _Sean A. Irvine_, May 19 2019