A179133 - OEIS

%I #23 Oct 08 2024 12:49:44

%S 2,4,5,26,68,89,466,1220,1597,8362,21892,28657,150050,392836,514229,

%T 2692538,7049156,9227465,48315634,126491972,165580141,866988874,

%U 2269806340,2971215073,15557484098,40730022148,53316291173,279167724890

%N Denominators of A178381(4*n+3)/A178381(4*n+2).

%C For the numerators see A128052.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,18,0,0,-1).

%F a(n) = A179134(n)*A153727(n+1)/2.

%F Lim_{n->infinity} A128052(n+1)/A179133(n) = 1+cos(Pi/5) = A296182.

%F From _Colin Barker_, Jun 27 2013: (Start)

%F G.f.: -(x^5+4*x^4+10*x^3-5*x^2-4*x-2)/((x^2-3*x+1)*(x^4+3*x^3+8*x^2+3*x+1)).

%F a(n) = 18*a(n-3)-a(n-6). (End)

%F From _Greg Dresden_, Oct 16 2021: (Start)

%F a(3*n) = 2*Fibonacci(6*n+1),

%F a(3*n+1) = 2*Fibonacci(6*n+3),

%F a(3*n+2) = Fibonacci(6*n+5). (End)

%p with(GraphTheory): nmax:=120; 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-1 do a(n):= denom(A178381(4*n+3)/A178381(4*n+2)) od: seq(a(n),n=0..nmax/4-1);

%t Flatten[Table[{2*Fibonacci[6 n + 1], 2*Fibonacci[6 n + 3],

%t Fibonacci[6 n + 5]}, {n, 0, 10}]] (* _Greg Dresden_, Oct 16 2021 *)

%t LinearRecurrence[{0,0,18,0,0,-1},{2,4,5,26,68,89},30] (* _Harvey P. Dale_, Oct 08 2024 *)

%Y Cf. A000045, A128052, A153727, A178381, A179131, A179132, A179133, A179134, A296182.

%K easy,frac,nonn

%O 0,1

%A _Johannes W. Meijer_, Jul 01 2010