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A179133
Denominators of A178381(4*n+3)/A178381(4*n+2).
7
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
0,1
COMMENTS
For the numerators see A128052.
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)
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 *)
KEYWORD
easy,frac,nonn
AUTHOR
Johannes W. Meijer, Jul 01 2010
STATUS
approved