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A274220 a(n) = (-cos(Pi/7)/cos(2*Pi/7))^n + (-cos(2*Pi/7)/cos(3*Pi/7))^n + (cos(3*Pi/7)/cos(Pi/7))^n. 6
3, -4, 10, -25, 66, -179, 493, -1369, 3818, -10672, 29865, -83626, 234237, -656205, 1838483, -5151080, 14432666, -40438941, 113306686, -317477255, 889550021, -2492461633, 6983719214, -19567941936, 54828148469, -153625048854, 430447808073, -1206087937261, 3379383275971, -9468821484028 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) is an integer.

This is other half of A215076.

REFERENCES

R. Witula, E. Hetmaniok, D. Slota, Sums of the powers of any order roots taken from the roots of a given polynomial, Proceedings of the Fifteenth International Conference on Fibonacci Numbers and Their Applications, Eger, Hungary, 2012.

LINKS

Colin Barker, 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, Full Description of Ramanujan Cubic Polynomials, Journal of Integer Sequences, Vol. 13 (2010), Article 10.5.7.

Roman Witula, Ramanujan Cubic Polynomials of the Second Kind, Journal of Integer Sequences, Vol. 13 (2010), Article 10.7.5.

Roman Witula, Ramanujan Type Trigonometric Formulae, Demonstratio Math. 45 (2012) 779-796.

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, 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 (-4,-3,1).

FORMULA

a(n) = -4*a(n-1)-3*a(n-2)+a(n-3).

G.f.: (3+8*x+3*x^2) / (1+4*x+3*x^2-x^3). - Colin Barker, Jun 14 2016

EXAMPLE

a(0) = 3, a(1) = -4, a(2) = 10, a(3) = -25.

MATHEMATICA

CoefficientList[Series[(3 + 8 x + 3 x^2)/(1 + 4 x + 3 x^2 - x^3), {x, 0, 29}], x] (* Michael De Vlieger, Jun 14 2016 *)

PROG

(PARI) Vec((3+8*x+3*x^2)/(1+4*x+3*x^2-x^3) + O(x^30)) \\ Colin Barker, Jun 14 2016

CROSSREFS

Cf. A215076, A033304, A094648, A274032.

Sequence in context: A143108 A169790 A014009 * A299881 A218293 A288110

Adjacent sequences:  A274217 A274218 A274219 * A274221 A274222 A274223

KEYWORD

sign,easy

AUTHOR

Kai Wang, Jun 14 2016

EXTENSIONS

Many terms corrected by Colin Barker, Jun 14 2016

STATUS

approved

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Last modified December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)