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A122572
a(n) = -14*a(n-1) - a(n-2), with a(1) = a(2) = 1.
1
1, 1, -15, 209, -2911, 40545, -564719, 7865521, -109552575, 1525870529, -21252634831, 296011017105, -4122901604639, 57424611447841, -799821658665135, 11140078609864049, -155161278879431551, 2161117825702177665, -30100488280951055759, 419245718107612602961
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
Gareth Jones and David Singerman, Belyi Functions, Hypermaps and Galois Groups, Bull. London Math. Soc., 28 (1996), 561-590.
Tanya Khovanova, Recursive Sequences
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
Sequence in context: A280160 A239991 A274563 * A028230 A067560 A019553
KEYWORD
sign,easy,changed
AUTHOR
Roger L. Bagula, Sep 17 2006
EXTENSIONS
Edited by N. J. A. Sloane, Dec 04 2006
STATUS
approved