1,3

Characteristic polynomial associated with the ellipic cubic invariant x^8+14*x^4+1.

Gareth Jones and David Singerman, Belyi Functions, Hypermaps and Galois Groups, Bull. London Math. Soc., 28 (1996), 561-590.

Henry MacKean and Victor Moll, Ellipic Curves, Cambridge University Press, New York, 1997, page 22

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

G.f.: x(1+15x)/(1+14x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 16 2008] [Corrected by Richard Choulet (richardchoulet(AT)yahoo.fr), Nov 21 2008]

a(n)=(1/3)*sqrt(3)*[ -7+4*sqrt(3)]^n-(1/3)*sqrt(3)*[ -7-4*sqrt(3)]^n+(1/2)*[ -7-4*sqrt(3)]^n+(1 /2)*[ -7+4*sqrt(3)]^n [From Paolo P. Lava (ppl(AT)spl.at), Nov 19 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) [From Richard Choulet (richardchoulet(AT)yahoo.fr), Nov 21 2008]

a(n)=(-1)^n*A028230(n-1), n>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 19 2009]

M = {{0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}, {-1, 0, 0, 0, -14, 0, 0, 0}}; v[1] = Table[1, {n, 1, 8}] v[n_] := v[n] = M.v[n - 1] a = Table[v[4*n][[1]], {n, 1, 25}]

Sequence in context: A089138 A051813 A028230 this_sequence A067560 A019553 A112496

Adjacent sequences: A122569 A122570 A122571 this_sequence A122573 A122574 A122575

sign

Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 17 2006

Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2006