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A122572
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a(1)=a(2)=1, a(n) = -14a(n-1) - a(n-2).
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1
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1, 1, -15, 209, -2911, 40545, -564719, 7865521, -109552575, 1525870529, -21252634831, 296011017105, -4122901604639, 57424611447841, -799821658665135, 11140078609864049, -155161278879431551, 2161117825702177665, -30100488280951055759, 419245718107612602961
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OFFSET
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1,3
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COMMENTS
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Characteristic polynomial associated with the elliptic cubic invariant x^8 + 14*x^4 + 1.
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REFERENCES
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Henry MacKean and Victor Moll, Elliptic Curves, Cambridge University Press, New York, 1997, page 22
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LINKS
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FORMULA
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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) = 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
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MATHEMATICA
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LinearRecurrence[{-14, -1}, {1, 1}, 30] (* Harvey P. Dale, Jul 30 2013 *)
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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