|
| |
|
|
A130196
|
|
Period 3: repeat 1 2 2.
|
|
19
|
|
|
|
1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
From Reinhard Zumkeller, Nov 12 2009: (Start)
Denominator of x(n)=x(n-1)+x(n-2), x(0)=0, x(1)=1/2; numerator=A167808;
a(n) = A131534(n)+A022003(n) = A080425(n)-A131534(n)+2 = A153727(n)/A131534(n). (End)
Continued fraction expansion of (5+sqrt(85))/10. - Klaus Brockhaus, May 07 2010
|
|
|
LINKS
|
Table of n, a(n) for n=0..104.
Index to sequences with linear recurrences with constant coefficients, signature (0,0,1).
|
|
|
FORMULA
|
a(0)=1, a(1)=a(2)=2, a(n+3) = a(n).
a(n)=(1/9)*{8*(n mod 3)+5*[(n+1) mod 3]+2*[(n+2) mod 3]}, with n>=0. - Paolo P. Lava, Aug 28 2007
G.f.: -(1+2*x+2*x^2)/(x-1)/(x^2+x+1). - R. J. Mathar, Nov 14 2007
Closed form: a(n)=5/3+(2/3)*[ -1/2-(1/2*I)*sqrt(3)]^(-2)*[ -1/2-(1/2*I)*sqrt(3)]^n+(2/3)*[ -1/2+(1/2*I) *sqrt(3)]^(-2)*[ -1/2+(1/2*I)*sqrt(3)]^n+(1/3)*[ -1/2-(1/2*I)*sqrt(3)]^n+(1/3)*[ -1/2 +(1/2*I)*sqrt(3)]^n+(2/3)*[ -1/2-(1/2*I)*sqrt(3)]^(-1)*[ -1/2-(1/2*I)*sqrt(3)]^n+(2/3 )*[ -1/2+(1/2*I)*sqrt(3)]^(-1)*[ -1/2+(1/2*I)*sqrt(3)]^n, with n>=0 and I=sqrt(-1). - Paolo P. Lava, Jul 17 2008
a(n) = (5-2*cos(2*pi*n/3))/3. - Jaume Oliver Lafont, Nov 23 2008
a(n) = 2 - 0^(n mod 3). - Reinhard Zumkeller, Nov 12 2009
a(n) = A011655(n) + 1; a(n) = (n^2 mod 3) + 1. - Boris Putievskiy, Feb 03 2013
|
|
|
PROG
|
(PARI) a(n)=2-0^(n%3) \\ Charles R Greathouse IV, Jun 01 2011
|
|
|
CROSSREFS
|
Cf. A177347 (decimal expansion of (5+sqrt(85))/10). - Klaus Brockhaus, May 07 2010
Sequence in context: A102297 A098398 A131714 * A158209 A119646 A024693
Adjacent sequences: A130193 A130194 A130195 * A130197 A130198 A130199
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Paul Curtz, Aug 05 2007
|
|
|
EXTENSIONS
|
More terms from Klaus Brockhaus, May 07 2010
|
|
|
STATUS
|
approved
|
| |
|
|
