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%I #15 Mar 18 2024 12:29:49
%S 1,1,2,3,6,10,20,35,70,127,254,474,948,1807,3614,6995,13990,27370,
%T 54740,107883,215766,427351,854702,1698458,3396916,6765175,13530350,
%U 26985675,53971350,107746282,215492564,430470899,860941798,1720537327,3441074654
%N a(n) = Sum_{k == floor(n/2) (mod 5)} C(n,k).
%C 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.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-6,-1,2).
%F a(n) = A000045(n+1)+A173126(n). a(2n) = A054877(2n); a(2n+1) = A052964(2n).
%F 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
%F 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
%e 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.
%o (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
%K nonn,easy
%O 0,3
%A _Henry Bottomley_, Feb 10 2010
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