Search: id:A006495
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%I A006495 M2880
%S A006495 1,1,3,11,7,41,117,29,527,1199,237,6469,11753,8839,76443,
%T A006495 108691,164833,873121,922077,2521451,9653287,6699319,34867797,
%U A006495 103232189,32125393,451910159,1064447283,130656229,5583548873
%V A006495 1,1,-3,-11,-7,41,117,29,-527,-1199,237,6469,11753,-8839,-76443,
%W A006495 -108691,164833,873121,922077,-2521451,-9653287,-6699319,34867797,
%X A006495 103232189,32125393,-451910159,-1064447283,130656229,5583548873
%N A006495 Real part of (1+2i)^n.
%C A006495 Row sums of the Euler related triangle A117411. Partial sums are A006495. 
               - Paul Barry (pbarry(AT)wit.ie), Mar 16 2006
%C A006495 Binomial transform of [1, 0, -4, 0, 16, 0, -64, 0, 256, 0, ...] =: powers 
               of -4 with interpolated zeros . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Dec 02 2008]
%D A006495 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006495 G. Berzsenyi, Gaussian Fibonacci numbers, Fib. Quart., 15 (1977), 233-236.
%H A006495 <a href="Sindx_Ga.html#gaussians">Index entries for Gaussian integers 
               and primes</a>
%F A006495 a(n)=(1/2)*((1+2I)^n+(1-2I)^n) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Oct 28 2002
%F A006495 G.f.: (1-x)/(1-2x+5x^2); a(n)=2a(n-1)-5a(n-2); a(n)=5^(n/2)*cos(n*atan(1/
               3)+pi*n/4); a(n)=sum{k=0..n, sum{j=0..n-k, C(n,k-j)*C(j,n-k)}*(-4)^(n-k)}; 
               - Paul Barry (pbarry(AT)wit.ie), Mar 16 2006
%F A006495 A000351(n) = a(n)^2 + A006496(n)^2. - Fabrice Baubet (intih(AT)free.fr), 
               May 28 2007
%F A006495 a(n)=Sum_{k, 0<=k<=n} A124182(n,k)*(-5)^(n-k). [From Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Nov 01 2008]
%F A006495 a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*(-4)^(n-k). [From Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Nov 14 2008]
%t A006495 Table[Re[(1+2I)^n],{n,0,29}] - Giovanni Resta (g.resta(AT)iit.cnr.it), 
               Mar 28 2006
%o A006495 sage: [lucas_number2(n,2,5)/2 for n in xrange(0,30)] - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jul 08 2008
%Y A006495 Cf. A006496.
%Y A006495 Sequence in context: A153285 A083557 A119324 this_sequence A112286 A126261 
               A050097
%Y A006495 Adjacent sequences: A006492 A006493 A006494 this_sequence A006496 A006497 
               A006498
%K A006495 sign
%O A006495 0,3
%A A006495 N. J. A. Sloane (njas(AT)research.att.com).
%E A006495 Signs from Christian G. Bower (bowerc(AT)usa.net), Nov 15 1998
%E A006495 Corrected by Giovanni Resta (g.resta(AT)iit.cnr.it), Mar 28 2006

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