OFFSET
0,1
COMMENTS
a(n) = (a/b)^n + (b/c)^n + (c/a)^n, where a = cos(Pi/13) + cos(5*Pi/13), b = cos(3*Pi/13) + cos(11*Pi/13), and c = cos(7*Pi/13) + cos(9*Pi/13).
The Berndt-type sequence number 11 for the argument 2Pi/13. I am very grateful to Sergey Markelov and LiveJournal for his and its respectively inspiration for creating this sequence.
LINKS
Sergey Markelov, Identity for Pi/19 cosines with cube roots, LiveJournal for Mathematics in Russian, 2012 (in Russian).
Index entries for linear recurrences with constant coefficients, signature (-10,-3,1).
FORMULA
a(n) = -10*a(n-1)-3*a(n-2)+a(n-3). G.f.: -(3*x^2+20*x+3) / (x^3-3*x^2-10*x-1). - Colin Barker, Jun 01 2013
MATHEMATICA
LinearRecurrence[{-10, -3, 1}, {3, -10, 94}, 20] (* T. D. Noe, Sep 17 2012 *)
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Roman Witula, Sep 15 2012
STATUS
approved