A107855 - OEIS

%I #11 Jul 31 2015 17:53:26

%S 1,1,1,0,1,1,2,3,1,10,9,33,24,109,85,360,275,1189,914,3927,3013,12970,

%T 9957,42837,32880,141481,108601,467280,358679,1543321,1184642,5097243,

%U 3912601,16835050,12922449,55602393,42679944,183642229,140962285

%N a(n) = 2*a(n-2)+4*a(n-4)+a(n-6), n>11.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 2, 0, 4, 0, 1).

%F lim_{ n->inf} a(n)/a(n-1) alternating between 0.767592... and 4.30278...

%F G.f.: x*(2*x^10+8*x^8+5*x^6+3*x^5+5*x^4+x^2-1+2*x^3-x)/( (x^2+1)*(x^4+3*x^2-1)). [ Sep 28 2009]

%F a(2n) = A006190(n-2), a(2n+1) = (1/3)*[A052924(n-2) - 4*(-1)^n], n>2.

%t F[1] = 1; F[2] = 1; F[3] = 1; F[4] = 0; F[n__] := F[n] = If[ Mod[n, 2] == 0, -3*F[n - 1] + 3*F[n - 3] + F[n - 4], F[n - 1] + F[n - 2]] a = Table[Abs[F[n]], {n, 1, 50}]

%t Join[{1,1,1,0,1},LinearRecurrence[{0,2,0,4,0,1},{1,2,3,1,10,9},50]] (* _Harvey P. Dale_, Oct 18 2013 *)

%K nonn,easy

%O 1,7

%A _Roger L. Bagula_, Jun 12 2005

%E Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009