OFFSET
0,1
COMMENTS
This is the other half of A274592.
a(n) is x1^n + x2^n + x3^n, where x1, x2, x3 are the roots of the polynomial
x^3 +25* x^2 + 31*x - 1.
x1 = (tan(2*Pi/7)*tan(4*Pi/7))/(tan(Pi/7))^2,
x2 = (tan(4*Pi/7)*tan(Pi/7))/(tan(2*Pi/7))^2,
x3 = (tan(Pi/7)*tan(2*Pi/7))(tan(4*Pi/7))^2.
LINKS
Colin Barker, Table of n, a(n) for n = 0..700
Index entries for linear recurrences with constant coefficients, signature (-25,-31,1).
FORMULA
a(n) = ((tan(Pi/7))^2/(tan(2*Pi/7)*tan(4*Pi/7)))^(-n)+((tan(2*Pi/7))^2/(tan(4*Pi/7)*tan(Pi/7)))^(-n)+((tan(4*Pi/7))^2/(tan(Pi/7)*tan(2*Pi/7)))^(-n).
a(n) = -25*a(n-1) - 31*a(n-2) + a(n-3).
G.f.: (3+50*x+31*x^2) / (1+25*x+31*x^2-x^3). - Colin Barker, Jul 01 2016
MATHEMATICA
CoefficientList[Series[(3 + 50 x + 31 x^2)/(1 + 25 x + 31 x^2 - x^3), {x, 0, 18}], x] (* Michael De Vlieger, Jul 01 2016 *)
PROG
(PARI) Vec((3+50*x+31*x^2)/(1+25*x+31*x^2-x^3) + O(x^20)) \\ Colin Barker, Jul 01 2016
(PARI) polsym(x^3 +25* x^2 + 31*x - 1, 30) \\ Charles R Greathouse IV, Jul 20 2016
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Kai Wang, Jul 01 2016
STATUS
approved