Search: id:A047946
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%I A047946
%S A047946 3,2,8,17,48,122,323,842,2208,5777,15128,39602,103683,271442,710648,
%T A047946 1860497,4870848,12752042,33385283,87403802,228826128,599074577,
%U A047946 1568397608,4106118242,10749957123,28143753122,73681302248
%N A047946 5*F(n)^2+3*(-1)^n where F(n) are the Fibonacci numbers A000045.
%C A047946 Form the matrix A=[1,1,1;2,1,0;1,0,0]. a(n)=trace(A^n). - Paul Barry 
               (pbarry(AT)wit.ie), Sep 22 2004
%C A047946 The set of prime divisors of elements of this sequence with the exception 
               of 3 is the set of primes that do not divide odd Fibonacci numbers. 
               - Tanya Khovanova (tanyakh(AT)yahoo.com), May 19 2008
%H A047946 Tanya Khovanova, <a href="http://blog.tanyakhovanova.com/?p=25">Divisibility 
               of Odd Fibonaccis</a>
%F A047946 a(n)=F(3n)/F(n), n>0; a(n)=2*a(n-1)+2*a(n-2)-a(n-3); a(n)=3a(n-1)-a(n-2)+5(-1)^n; 
               a(n) = L(2n) + (-1)^n, where the L(n) are Lucas numbers A000032. 
               G.f.: (3-4*x-2*x^2)/(1-2*x-2*x^2+x^3).
%F A047946 for n>0 a(n)=A000045(3n)/A000045(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Aug 30 2003
%F A047946 a(n)=[3/2+(1/2)*sqrt(5)]^n+(-1)^n+[3/2-(1/2)*sqrt(5)]^n, with n>=0 - 
               Paolo P. Lava (ppl(AT)spl.at), Jun 12 2008
%o A047946 (PARI) a(n)=5*fibonacci(n)^2+3*(-1)^n
%Y A047946 Cf. A000045, A000032.
%Y A047946 Second row of array A028412.
%Y A047946 Cf. A133247 = prime numbers p with property that no odd Fibonacci number 
               is divisible by p.
%Y A047946 Sequence in context: A088551 A165660 A107300 this_sequence A066045 A110866 
               A060481
%Y A047946 Adjacent sequences: A047943 A047944 A047945 this_sequence A047947 A047948 
               A047949
%K A047946 nonn,easy
%O A047946 0,1
%A A047946 John W. Layman (layman(AT)math.vt.edu (5/21/99))
%E A047946 Entry improved by comments from Michael Somos.

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