Search: id:A122571
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%I A122571
%S A122571 1,1,13,181,2521,35113,489061,6811741,94875313,1321442641,18405321661,
%T A122571 256353060613,3570537526921,49731172316281,692665874901013,
%U A122571 9647591076297901,134373609193269601,1871582937629476513
%N A122571 a(1)=a(2)=1, a(n)=14a(n-1)-a(n-2).
%C A122571 Each term is a sum of two consecutive squares, or a(n) = k^2 + (k+1)^2 
               for some k. Squares of each term are the hex numbers, or centered 
               hexagonal numbers: a(n) = A001570(n-1) for n>1. - Alexander Adamchuk 
               (alex(AT)kolmogorov.com), Apr 14 2008
%D A122571 Gareth Jones and David Singerman, Belyi Functions, Hypermaps and Galois 
               Groups, Bull. London Math. Soc., 28 (1996), 561-590.
%D A122571 Henry MacKean and Victor Moll, Ellipic Curves, Cambridge University Press, 
               New York, 1997, page 22.
%H A122571 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A122571 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A122571 Let M be the 8 X 8 matrix {{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}}; let v[1] = Table[1, {n, 1, 8}], 
               v[n] = M.v[n - 1]; then a(n) =v[4*n][[1]].
%F A122571 a(n)=(1/4)*sqrt(3)*[7-4*sqrt(3)]^n-(1/4)*sqrt(3)*[7+4*sqrt(3)]^n+(1/2)*[7+4*sqrt(3)]^n+(1/
               2) *[7-4*sqrt(3)]^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jun 
               19 2008
%F A122571 G.f.: x*(1-13x)/(1-14*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 17 2008]
%t A122571 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 A122571 This is simply a variant of A001570.
%Y A122571 Sequence in context: A127390 A142646 A083576 this_sequence A001570 A020544 
               A009015
%Y A122571 Adjacent sequences: A122568 A122569 A122570 this_sequence A122572 A122573 
               A122574
%K A122571 nonn
%O A122571 1,3
%A A122571 Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 17 2006
%E A122571 Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 21 2006 and 
               Dec 04 2006

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