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Search: id:A006496
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| A006496 |
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Imaginary part of (1+2i)^n.
(Formerly M0933)
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+0
6
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| 0, 2, 4, -2, -24, -38, 44, 278, 336, -718, -3116, -2642, 10296, 33802, 16124, -136762, -354144, -24478, 1721764, 3565918, -1476984, -20783558, -34182196, 35553398, 242017776, 306268562, -597551756, -2726446322, -2465133864, 8701963882, 29729597084, 15949374758
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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G. Berzsenyi, Gaussian Fibonacci numbers, Fib. Quart., 15 (1977), 233-236.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Index entries for Gaussian integers and primes
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FORMULA
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a(0)=0, a(1)=2, a(n)=2a(n-1)-5a(n-2) - T. D. Noe (noe(AT)sspectra.com), Nov 09 2006
For all n, a(n) = - [M^n]_1,2, where M = [1, -2; 2, 1]. - Simone Severini (simoseve(AT)gmail.com), Apr 25 2007
A000351(n) = A006495(n)^2 + a(n)^2. - Fabrice Baubet (intih(AT)free.fr), May 28 2007
O.g.f.: 2*x/(1-2*x+5*x^2). a(n)=2*A045873(n). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 06 2008
a(n)=(1/2)*I*(1-2*I)^n-(1/2)*I*(1+2*I)^n, with n>=0 and I=sqrt(-1) [From Paolo P. Lava (ppl(AT)spl.at), Oct 03 2008]
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CROSSREFS
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Cf. A006495.
Sequence in context: A152878 A100944 A059890 this_sequence A130172 A029589 A121819
Adjacent sequences: A006493 A006494 A006495 this_sequence A006497 A006498 A006499
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Signs from Christian G. Bower (bowerc(AT)usa.net), Nov 15 1998
Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 09 2006
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 06 2008
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