0,3

Row sums of the Euler related triangle A117411. Partial sums are A006495. - Paul Barry (pbarry(AT)wit.ie), Mar 16 2006

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]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

G. Berzsenyi, Gaussian Fibonacci numbers, Fib. Quart., 15 (1977), 233-236.

Index entries for Gaussian integers and primes

a(n)=(1/2)*((1+2I)^n+(1-2I)^n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 28 2002

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

A000351(n) = a(n)^2 + A006496(n)^2. - Fabrice Baubet (intih(AT)free.fr), May 28 2007

a(n)=Sum_{k, 0<=k<=n} A124182(n,k)*(-5)^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 01 2008]

a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*(-4)^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 14 2008]

Table[Re[(1+2I)^n], {n, 0, 29}] - Giovanni Resta (g.resta(AT)iit.cnr.it), Mar 28 2006

sage: [lucas_number2(n, 2, 5)/2 for n in xrange(0, 30)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2008

Cf. A006496.

Sequence in context: A153285 A083557 A119324 this_sequence A112286 A126261 A050097

Adjacent sequences: A006492 A006493 A006494 this_sequence A006496 A006497 A006498

sign

N. J. A. Sloane (njas(AT)research.att.com).

Signs from Christian G. Bower (bowerc(AT)usa.net), Nov 15 1998

Corrected by Giovanni Resta (g.resta(AT)iit.cnr.it), Mar 28 2006