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 A179135 a(n) = (3-sqrt(5))*((3+sqrt(5))/10)^(-n)/2+(3+sqrt(5))*((3-sqrt(5))/10)^(-n)/2. 3

%I

%S 3,35,450,5875,76875,1006250,13171875,172421875,2257031250,

%T 29544921875,386748046875,5062597656250,66270263671875,

%U 867489013671875,11355578613281250,148646453857421875,1945807342529296875

%N a(n) = (3-sqrt(5))*((3+sqrt(5))/10)^(-n)/2+(3+sqrt(5))*((3-sqrt(5))/10)^(-n)/2.

%F a(n) = A178381(4*n+3).

%F G.f.: (3-10*z)/(1-15*z+25*z^2).

%F Limit(a(n+k)/a(k), k=infinity) = A000351(n)*A130196(n)/(A128052(n) - A167808(2*n)*sqrt(5)).

%F Limit(A128052(n)/A167808(2*n),n=infinity) = sqrt(5).

%F a(n) = 5^n*Lucas(2*(n+1)). - _Ehren Metcalfe_, Apr 22 2018

%p with(GraphTheory): nmax:=72; P:=9: G:=PathGraph(P): A:= AdjacencyMatrix(G): for n from 0 to nmax do B(n):=A^n; A178381(n):=add(B(n)[1,k],k=1..P); od: for n from 0 to nmax/4-1 do a(n):= A178381(4*n+3) od: seq(a(n),n=0..nmax/4-1);

%Y Cf. A109106.

%K easy,nonn

%O 0,1

%A _Johannes W. Meijer_, Jul 01 2010

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Last modified October 21 16:25 EDT 2019. Contains 328302 sequences. (Running on oeis4.)