Search: id:A001607
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%I A001607 M2225 N0883
%S A001607 0,1,1,1,3,1,5,7,3,17,11,23,45,1,91,89,93,271,85,457,627,287,
%T A001607 1541,967,2115,4049,181,8279,7917,8641,24475,7193,41757,
%U A001607 56143,27371,139657,84915,194399,364229,24569,753027,703889
%V A001607 0,1,-1,-1,3,-1,-5,7,3,-17,11,23,-45,-1,91,-89,-93,271,-85,-457,627,287,
%W A001607 -1541,967,2115,-4049,-181,8279,-7917,-8641,24475,-7193,-41757,
%X A001607 56143,27371,-139657,84915,194399,-364229,-24569,753027,-703889
%N A001607 a(n) = - a(n-1) - 2a(n-2).
%C A001607 x/(x^2+x+2)=sum(n=0,inf,a(n)*(x/2)^n) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Mar 12 2002
%C A001607 4*2^n = A002249(n)^2+7*A001607(n)^2. See A077020, A077021.
%C A001607 Apart from the sign, this is an example of a sequence of Lehmer numbers. 
               In this case, the two parameters, alpha and beta, are (1 +- i Sqrt(7))/
               2. Bilu, Hanrot, Voutier and Mignotte show that all terms of a Lehmer 
               sequence a(n) have a primitive factor for n > 30. Note that for this 
               sequence, a(30) = 24475 = 5*5*11*89 has no primitive factors. - T. 
               D. Noe (noe(AT)sspectra.com), Oct 29 2003
%D A001607 D. Jarden, Recurring Sequences. Riveon Lematematika, Jerusalem, 1966.
%D A001607 Erwin Just, Problem E2367, Amer. Math. Monthly, 79 (1972), 772.
%D A001607 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001607 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001607 Y. Bilu, G. Hanrot, P. M. Voutier and M. Mignotte, <a href="http://www.inria.fr/
               rrrt/rr-3792.html">Existence of primitive divisors of Lucas and Lehmer 
               numbers</a>
%H A001607 G. P. Michon, <a href="http://www.numericana.com/answer/numbers.htm#m">
               Never Back to -1</a>.
%H A001607 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LehmerNumber.html">Lehmer Number</a>
%F A001607 G.f.: x/(1+x+2*x^2).
%F A001607 a(n) = Sum_{k=0..n-1} (-1)^(n-k-1)*binomial(n-k-1, k)*2^k = -2/sqrt(7)*(-sqrt(2))^n*(sin(n*arctan(sqrt(7)))).\
                - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 05 2003
%o A001607 (PARI) a(n)=if(n<0,0,polcoeff(x/(1+x+2*x^2)+x*O(x^n),n))
%o A001607 (PARI) a(n)=if(n<0,0,2*imag(((-1+quadgen(-28))/2)^n))
%Y A001607 Apart from signs, same as A077020.
%Y A001607 Sequence in context: A038871 A143524 A134249 this_sequence A167433 A077020 
               A107920
%Y A001607 Adjacent sequences: A001604 A001605 A001606 this_sequence A001608 A001609 
               A001610
%K A001607 sign,easy
%O A001607 0,5
%A A001607 N. J. A. Sloane (njas(AT)research.att.com).

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