A216241 Number of n-step walks (each step +-1 starting from 0) which are never more than 5 or less than -5.

1, 2, 4, 8, 16, 32, 62, 124, 236, 472, 890, 1780, 3340, 6680, 12502, 25004, 46732, 93464, 174554, 349108, 651740, 1303480, 2432918, 4865836, 9080956, 18161912, 33892954, 67785908, 126494956, 252989912, 472095062, 944190124, 1761901676, 3523803352, 6575544410, 13151088820

Offset: 0

Author

Philippe Deléham, Mar 15 2013

Keywords

• nonn
• walk
• easy

Crossrefs

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

Programs

Mathematica

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 *)

Formula

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

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

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

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

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

a(n) = Sum_{k=0..n} A214846(n-k, k). - Philippe Deléham, Mar 25 2013

Extensions

a(34) corrected by Sean A. Irvine, May 19 2019