A216450 a(n) = -10*a(n-1) - 3*a(n-2) + a(n-3) with a(0) = 3, a(1) = -10, and a(2) = 94.

3, -10, 94, -907, 8778, -84965, 822409, -7960417, 77051978, -745816120, 7219044849, -69875948152, 676356530853, -6546718419225, 63368238651539, -613365874726862, 5937007312894778, -57466607266115655, 556241684847745354, -5384080019366211797

Offset: 0

Author

Roman Witula, Sep 15 2012

Keywords

• sign
• easy

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).

Programs

Mathematica

LinearRecurrence[{-10, -3, 1}, {3, -10, 94}, 20] (* T. D. Noe, Sep 17 2012 *)

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