A179133 Denominators of A178381(4*n+3)/A178381(4*n+2).

2, 4, 5, 26, 68, 89, 466, 1220, 1597, 8362, 21892, 28657, 150050, 392836, 514229, 2692538, 7049156, 9227465, 48315634, 126491972, 165580141, 866988874, 2269806340, 2971215073, 15557484098, 40730022148, 53316291173, 279167724890

Offset: 0

Author

Johannes W. Meijer, Jul 01 2010

Keywords

• easy
• frac
• nonn

Comments

For the numerators see A128052.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,18,0,0,-1).

Crossrefs

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

Programs

Maple

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);

Mathematica

Flatten[Table[{2*Fibonacci[6 n + 1], 2*Fibonacci[6 n + 3],
Fibonacci[6 n + 5]}, {n, 0, 10}]] (* Greg Dresden, Oct 16 2021 *)
LinearRecurrence[{0,0,18,0,0,-1},{2,4,5,26,68,89},30] (* Harvey P. Dale, Oct 08 2024 *)

Formula

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

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

From Colin Barker, Jun 27 2013: (Start)

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)).

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

From Greg Dresden, Oct 16 2021: (Start)

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

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

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