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Search: id:A047946
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| A047946 |
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5*F(n)^2+3*(-1)^n where F(n) are the Fibonacci numbers A000045. |
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+0
2
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| 3, 2, 8, 17, 48, 122, 323, 842, 2208, 5777, 15128, 39602, 103683, 271442, 710648, 1860497, 4870848, 12752042, 33385283, 87403802, 228826128, 599074577, 1568397608, 4106118242, 10749957123, 28143753122, 73681302248
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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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
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
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LINKS
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Tanya Khovanova, Divisibility of Odd Fibonaccis
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FORMULA
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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).
for n>0 a(n)=A000045(3n)/A000045(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 30 2003
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
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PROGRAM
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(PARI) a(n)=5*fibonacci(n)^2+3*(-1)^n
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CROSSREFS
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Cf. A000045, A000032.
Second row of array A028412.
Cf. A133247 = prime numbers p with property that no odd Fibonacci number is divisible by p.
Sequence in context: A088551 A165660 A107300 this_sequence A066045 A110866 A060481
Adjacent sequences: A047943 A047944 A047945 this_sequence A047947 A047948 A047949
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KEYWORD
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nonn,easy
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu (5/21/99))
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EXTENSIONS
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Entry improved by comments from Michael Somos.
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