%I A006496 M0933
%S A006496 0,2,4,2,24,38,44,278,336,718,3116,2642,10296,33802,16124,136762,354144,
               24478,
%T A006496 1721764,3565918,1476984,20783558,34182196,35553398,242017776,306268562,
               597551756,
%U A006496 2726446322,2465133864,8701963882,29729597084,15949374758
%V A006496 0,2,4,-2,-24,-38,44,278,336,-718,-3116,-2642,10296,33802,16124,-136762,
               -354144,-24478,
%W A006496 1721764,3565918,-1476984,-20783558,-34182196,35553398,242017776,306268562,
               -597551756,
%X A006496 -2726446322,-2465133864,8701963882,29729597084,15949374758
%N A006496 Imaginary part of (1+2i)^n.
%D A006496 G. Berzsenyi, Gaussian Fibonacci numbers, Fib. Quart., 15 (1977), 233-236.
%D A006496 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A006496 <a href="Sindx_Ga.html#gaussians">Index entries for Gaussian integers 
               and primes</a>
%F A006496 a(0)=0, a(1)=2, a(n)=2a(n-1)-5a(n-2) - T. D. Noe (noe(AT)sspectra.com), 
               Nov 09 2006
%F A006496 For all n, a(n) = - [M^n]_1,2, where M = [1, -2; 2, 1]. - Simone Severini 
               (simoseve(AT)gmail.com), Apr 25 2007
%F A006496 A000351(n) = A006495(n)^2 + a(n)^2. - Fabrice Baubet (intih(AT)free.fr), 
               May 28 2007
%F A006496 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
%F A006496 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]
%Y A006496 Cf. A006495.
%Y A006496 Sequence in context: A152878 A100944 A059890 this_sequence A130172 A029589 
               A121819
%Y A006496 Adjacent sequences: A006493 A006494 A006495 this_sequence A006497 A006498 
               A006499
%K A006496 sign
%O A006496 0,2
%A A006496 N. J. A. Sloane (njas(AT)research.att.com).
%E A006496 Signs from Christian G. Bower (bowerc(AT)usa.net), Nov 15 1998
%E A006496 Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 09 2006
%E A006496 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 06 2008