A173125 a(n) = Sum_{k == floor(n/2) (mod 5)} C(n,k).

1, 1, 2, 3, 6, 10, 20, 35, 70, 127, 254, 474, 948, 1807, 3614, 6995, 13990, 27370, 54740, 107883, 215766, 427351, 854702, 1698458, 3396916, 6765175, 13530350, 26985675, 53971350, 107746282, 215492564, 430470899, 860941798, 1720537327, 3441074654

Offset

0,3

Comments

Greater of number of closed walks of length n from a node on a pentagon and number of walks of length n between two adjacent nodes on a pentagon.

Links

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (2,3,-6,-1,2).

Formula

a(n) = A000045(n+1)+A173126(n). a(2n) = A054877(2n); a(2n+1) = A052964(2n).

a(n) = 2*a(n-1)+3*a(n-2)-6*a(n-3)-a(n-4)+2*a(n-5). - Colin Barker, Sep 14 2014

G.f.: -(x-1)*(x^3+3*x^2-1) / ((2*x-1)*(x^2-x-1)*(x^2+x-1)). - Colin Barker, Sep 14 2014

Example

For n=15, k=7 mod 5 gives k=2, 7 or 12, and C(15,2)+C(15,7)+C(15,12) = 105+6435+455, so a(15)=6995.

Prog

(PARI) Vec(-(x-1)*(x^3+3*x^2-1)/((2*x-1)*(x^2-x-1)*(x^2+x-1)) + O(x^100)) \\ Colin Barker, Sep 14 2014

Crossrefs

Sequence in context: A126930 A210736 A036557 * A047131 A231331 A008927

Adjacent sequences: A173122 A173123 A173124 * A173126 A173127 A173128

Keyword

nonn,easy

Author

Henry Bottomley, Feb 10 2010

Status

approved