A173126 sum_{k=floor[(n+5)/2] mod 5} C(n,k)

0, 0, 0, 0, 1, 2, 7, 14, 36, 72, 165, 330, 715, 1430, 3004, 6008, 12393, 24786, 50559, 101118, 204820, 409640, 826045, 1652090, 3321891, 6643782, 13333932, 26667864, 53457121, 106914242, 214146295, 428292590, 857417220, 1714834440, 3431847189

Offset

0,6

Comments

Lesser 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) =A173125(n)-A000045(n+1). a(2n) =A052964(2n-1); a(2n+1) =A054877(2n+1) =2*a(2n).

a(n)= 2*a(n-1) +3*a(n-2) -6*a(n-3) -a(n-4) +2*a(n-5). G.f.: x^4/((1-2*x) * (x^2+x-1) * (x^2-x-1)). [From R. J. Mathar, Feb 19 2010]

Example

For n=15, k=10 mod 5 gives k=0, 5, 10, or 15, and C(15,0)+C(15,5)+C(15,10)+C(15,15) = 1+3003+3003+1, so a(15)=6008

Mathematica

LinearRecurrence[{2, 3, -6, -1, 2}, {0, 0, 0, 0, 1}, 40] (* Harvey P. Dale, May 05 2018 *)

Crossrefs

Sequence in context: A060552 A274868 A191396 * A256272 A320651 A167762

Adjacent sequences: A173123 A173124 A173125 * A173127 A173128 A173129

Keyword

nonn

Author

Henry Bottomley, Feb 10 2010

Status

approved