OFFSET
1,2
COMMENTS
a(n)/a(n-1) tends to 1 / cos(4*Pi/9) = 5.758770483..., which is an eigenvalue of the matrix M, which is derived from the polynomial 8x^3 - 6x + 1 (having roots cos(2*Pi/9), cos(4*Pi/9), and cos(8*Pi/9)).
REFERENCES
C. V. Durell & A. Robson, "Advanced Trigonometry", Dover 2003, p. 208.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (6,0,-8).
FORMULA
G.f.: x*(1-4*x+8*x^2+16*x^3)/(1-6*x+8*x^3). [Colin Barker, Feb 01 2012]
EXAMPLE
a(4), a(5), a(6) are found in M^5 * [1 1 1] = [128 752 4352].
MATHEMATICA
Table[ Abs[ MatrixPower[{{6, 0, -8}, {1, 0, 0}, {0, 1, 0}}, n].{1, 1, 1}][[2]], {n, 21}] (* Robert G. Wilson v, Apr 28 2004 *)
PROG
(PARI) Vec(x*(1-4*x+8*x^2+16*x^3)/(1-6*x+8*x^3)+O(x^99)) \\ Charles R Greathouse IV, Feb 01 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Apr 25 2004
EXTENSIONS
More terms from Robert G. Wilson v, Apr 28 2004
STATUS
approved