Search: id:A122572
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%I A122572
%S A122572 1,1,15,209,2911,40545,564719,7865521,109552575,1525870529,21252634831,
%T A122572 296011017105,4122901604639,57424611447841,799821658665135,11140078609864049,
%U A122572 155161278879431551,2161117825702177665,30100488280951055759,419245718107612602961
%V A122572 1,1,-15,209,-2911,40545,-564719,7865521,-109552575,1525870529,-21252634831,
%W A122572 296011017105,-4122901604639,57424611447841,-799821658665135,11140078609864049,
%X A122572 -155161278879431551,2161117825702177665,-30100488280951055759,419245718107612602961
%N A122572 a(1)=a(2)=1, a(n)=-14a(n-1)-a(n-2)
%C A122572 Characteristic polynomial associated with the ellipic cubic invariant 
               x^8+14*x^4+1.
%D A122572 Gareth Jones and David Singerman, Belyi Functions, Hypermaps and Galois 
               Groups, Bull. London Math. Soc., 28 (1996), 561-590.
%D A122572 Henry MacKean and Victor Moll, Ellipic Curves, Cambridge University Press, 
               New York, 1997, page 22
%H A122572 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A122572 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A122572 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]
%F A122572 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]
%F A122572 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]
%F A122572 a(n)=(-1)^n*A028230(n-1), n>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Mar 19 2009]
%t A122572 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}]
%Y A122572 Sequence in context: A089138 A051813 A028230 this_sequence A067560 A019553 
               A112496
%Y A122572 Adjacent sequences: A122569 A122570 A122571 this_sequence A122573 A122574 
               A122575
%K A122572 sign
%O A122572 1,3
%A A122572 Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 17 2006
%E A122572 Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2006

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