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 A173126 sum_{k=floor[(n+5)/2] mod 5} C(n,k) 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 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 A167762 A191389 Adjacent sequences:  A173123 A173124 A173125 * A173127 A173128 A173129 KEYWORD nonn AUTHOR Henry Bottomley, Feb 10 2010 STATUS approved

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Last modified August 19 15:56 EDT 2018. Contains 313880 sequences. (Running on oeis4.)