This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A274032 Sum of n-th powers of the roots of x^3 + 9*x^2 - x - 1. 8
 3, -9, 83, -753, 6851, -62329, 567059, -5159009, 46935811, -427014249, 3884905043, -35344223825, 321555905219, -2925462465753, 26615373873171, -242142271419073, 2202970354179075, -20042260085157577, 182341168849178195, -1658909809373582257 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS A Berndt-type sequence for tan(2*Pi/7). a(n) is always an integer. a(n) is x1^n + x2^n + x3^n, where x1, x2, x3 are the roots of the polynomial x^3 + 9*x^2 - x - 1. x1 = tan(Pi/7)/tan(2*Pi/7), x2 = tan(2*Pi/7)/tan(4*Pi/7), x3 = tan(4*Pi/7)/tan(Pi/7). This is a two sided sequence. The other half is A274075. - Kai Wang, Aug 02 2016 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 B. C. Berndt, L.-C. Zhang, Ramanujan's identities for eta-functions, Math. Ann. 292 (1992), 561-573. Roman Witula, Ramanujan Type Trigonometric Formulas: The General Form for the Argument 2Pi/7, J. Integer Seq., 12 (2009), Article 09.8.5. Roman Witula and Damian Slota, New Ramanujan-Type Formulas and Quasi-Fibonacci Numbers of Order 7, Journal of Integer Sequences, Vol. 10 (2007), Article 07.5.6 Roman Witula and Damian Slota, Quasi-Fibonacci Numbers of Order 11, Journal of Integer Sequences, Vol. 10 (2007), Article 07.8.5 Roman Witula, Damian Slota and Adam Warzynski, Quasi-Fibonacci Numbers of the Seventh Order, J. Integer Seq., 9 (2006), Article 06.4.3. Index entries for linear recurrences with constant coefficients, signature (-9,1,1). FORMULA a(n) = (tan(Pi/7)/tan(2*Pi/7))^n + (-tan(2*Pi/7)/tan(3*Pi/7))^n + (-tan(3*Pi/7)/tan(Pi/7))^n. From Colin Barker, Jun 07 2016: (Start) a(n) = -9*a(n-1)+a(n-2)+a(n-3) for n>2. G.f.: (3+18*x-x^2) / (1+9*x-x^2-x^3). (End) PROG (PARI) Vec((3+18*x-x^2)/(1+9*x-x^2-x^3) + O(x^30)) \\ Colin Barker, Jun 07 2016 (PARI) polsym(x^3 + 9*x^2 - x - 1, 30) \\ Charles R Greathouse IV, Jul 20 2016 CROSSREFS Cf. A033304, A094648, A215076, A274075. Sequence in context: A218149 A011764 A018624 * A032078 A307799 A326159 Adjacent sequences:  A274029 A274030 A274031 * A274033 A274034 A274035 KEYWORD sign,easy AUTHOR Kai Wang, Jun 07 2016 EXTENSIONS Edited by N. J. A. Sloane, Jun 07 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 26 20:24 EDT 2019. Contains 324380 sequences. (Running on oeis4.)