A094254 Let M be the 3 X 3 matrix [ 6 0 -8 / 1 0 0 / 0 1 0]. Then M^n * [1 1 1] = [a(n-1), a(n), a(n+1)].

1, 2, 20, 128, 752, 4352, 25088, 144512, 832256, 4792832, 27600896, 158947328, 915341312, 5271240704, 30355865600, 174812463104, 1006704852992, 5797382193152, 33385793454080, 192261121900544, 1107187673858048

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

Sequence in context: A350549 A062189 A203605 * A093647 A244887 A279112

Adjacent sequences: A094251 A094252 A094253 * A094255 A094256 A094257

Keyword

nonn,easy

Author

Gary W. Adamson, Apr 25 2004

Extensions

More terms from Robert G. Wilson v, Apr 28 2004

Status

approved