A287396 a(n) = (7*(csc(2*Pi/7))^2)^n + (7*(csc(4*Pi/7))^2)^n + (7*(csc(8*Pi/7))^2)^n.

3, 56, 1568, 53312, 1931776, 71300096, 2645479424, 98305622016, 3654656065536, 135885355483136, 5052615982317568, 187873377732526080, 6985794697679601664, 259756778648305139712, 9658687473893481906176, 359144636249686988029952, 13354285908291066433372160

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..600

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 (56,-784,3136).

Formula

a(n) = x1^n + x2^n + x3^n, where x1, x2, x3 are the roots of x^3 - 56*x^2 + 784* x - 3136, x1 = 7*(csc(2*Pi/7))^2, x2 = 7*(csc(4*Pi/7))^2, x3 = 7*(csc(8*Pi/7))^2.

a(n) = 56*a(n-1) - 784*a(n-2) + 3136*a(n-3) for n>2, a(0) = 3, a(1) = 56, a(2) = 1568.

G.f.: (3 - 28*x)*(1 - 28*x) / (1 - 56*x + 784*x^2 - 3136*x^3). - Colin Barker, May 25 2017

Mathematica

LinearRecurrence[{56, -784, 3136}, {3, 56, 1568}, 30] (* Harvey P. Dale, Aug 08 2017 *)

Prog

(PARI) Vec((3 - 28*x)*(1 - 28*x) / (1 - 56*x + 784*x^2 - 3136*x^3) + O(x^30)) \\ Colin Barker, May 25 2017
(PARI) polsym(x^3 - 56*x^2 + 784* x - 3136, 20) \\ Joerg Arndt, May 26 2017

Crossrefs

Cf. A033304, A094648, A274220, A215076, A274075, A274032, A275195, A215575, A274975.

Sequence in context: A160876 A241136 A202029 * A335804 A070731 A132489

Adjacent sequences: A287393 A287394 A287395 * A287397 A287398 A287399

Keyword

nonn,easy

Author

Kai Wang, May 24 2017

Status

approved