OFFSET
1,3
COMMENTS
Characteristic polynomial associated with the elliptic cubic invariant x^8 + 14*x^4 + 1.
REFERENCES
Henry MacKean and Victor Moll, Elliptic Curves, Cambridge University Press, New York, 1997, page 22
LINKS
Indranil Ghosh, Table of n, a(n) for n = 1..874
Gareth Jones and David Singerman, Belyi Functions, Hypermaps and Galois Groups, Bull. London Math. Soc., 28 (1996), 561-590.
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (-14,-1).
FORMULA
G.f.: x*(1+15*x)/(1+14*x+x^2). - Philippe Deléham, Nov 16 2008 [Corrected by Richard Choulet, Nov 21 2008]
a(n) = ((3+2*sqrt(3))/6)*(-7+4*sqrt(3))^(n-1)+((3-2*sqrt(3))/6)*(-7-4*sqrt(3))^(n-1) (n>=1). - Richard Choulet, Nov 21 2008
a(n) = (-1)^n*A028230(n-1), n>1. - R. J. Mathar, Mar 19 2009
a(n) = b such that (-1)^(2*n-3)*Integral_{x=0..Pi/2} cos((2*n-3)*x)/(2+sin(x)) dx = c + b*(log(2)-log(3)). - Francesco Daddi, Aug 01 2011
E.g.f.: 15 - exp(-7*x)*( 15*cosh(4*sqrt(3)*x) + (26*sqrt(3)/3)*sinh(4*sqrt(3)*x) ). - G. C. Greubel, Oct 29 2024
MATHEMATICA
LinearRecurrence[{-14, -1}, {1, 1}, 30] (* Harvey P. Dale, Jul 30 2013 *)
PROG
(Magma) [n le 2 select 1 else -14*Self(n-1) -Self(n-2): n in [1..41]]; // G. C. Greubel, Oct 29 2024
(SageMath)
A122572=BinaryRecurrenceSequence(-14, -1, 1, 1)
[A122572(n-1) for n in range(1, 41)] # G. C. Greubel, Oct 29 2024
CROSSREFS
KEYWORD
sign,easy,changed
AUTHOR
Roger L. Bagula, Sep 17 2006
EXTENSIONS
Edited by N. J. A. Sloane, Dec 04 2006
STATUS
approved