|
Search: id:A006495
|
|
|
| A006495 |
|
Real part of (1+2i)^n.
(Formerly M2880)
|
|
+0
12
|
|
| 1, 1, -3, -11, -7, 41, 117, 29, -527, -1199, 237, 6469, 11753, -8839, -76443, -108691, 164833, 873121, 922077, -2521451, -9653287, -6699319, 34867797, 103232189, 32125393, -451910159, -1064447283, 130656229, 5583548873
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Row sums of the Euler related triangle A117411. Partial sums are A006495. - Paul Barry (pbarry(AT)wit.ie), Mar 16 2006
|
|
REFERENCES
|
G. Berzsenyi, Gaussian Fibonacci numbers, Fib. Quart., 15 (1977), 233-236.
|
|
LINKS
|
Index entries for Gaussian integers and primes
Zerinvary Lajos, Sage Notebooks
|
|
FORMULA
|
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
|
|
MATHEMATICA
|
Table[Re[(1+2I)^n], {n, 0, 29}] - Giovanni Resta (g.resta(AT)iit.cnr.it), Mar 28 2006
|
|
PROGRAM
|
sage: [lucas_number2(n, 2, 5)/2 for n in xrange(0, 30)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2008
|
|
CROSSREFS
|
Cf. A006496.
Sequence in context: A094900 A083557 A119324 this_sequence A112286 A126261 A050097
Adjacent sequences: A006492 A006493 A006494 this_sequence A006496 A006497 A006498
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
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
|
|
|
Search completed in 0.005 seconds
|
