|
|
A177704
|
|
Period 4: repeat [1, 1, 1, 2].
|
|
11
|
|
|
1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
Continued fraction expansion of (3 + 2*sqrt(6))/5.
Decimal expansion of 1112/9999.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (5-(-1)^n + i*i^n-i*(-i)^n)/4 where i = sqrt(-1).
a(n) = a(n-4) for n > 3; a(0) = 1, a(1) = 1, a(2) = 1, a(3) = 2.
G.f.: (1+x+x^2+2*x^3)/(1-x^4).
a(n) = 1 + (1-(-1)^n) * (1+i^(n+1))/4 where i = sqrt(-1). - Bruno Berselli, Apr 05 2011
a(n) = 5/4 - sin(Pi*n/2)/2 - (-1)^n/4. - R. J. Mathar, Oct 08 2011
Sum_{i=0..n-1} a(i) = A001068(n). (End)
E.g.f.: (-sin(x) + 3*sinh(x) + 2*cosh(x))/2. - Ilya Gutkovskiy, Jun 15 2016
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[Floor[(n + 1)*5/4] - Floor[n*5/4], {n, 0, 100}] (* Wesley Ivan Hurt, Jun 15 2016 *)
LinearRecurrence[{0, 0, 0, 1}, {1, 1, 1, 2}, 100] (* Vincenzo Librandi, Jun 16 2016 *)
|
|
PROG
|
(Magma) &cat[ [1, 1, 1, 2]: k in [1..27] ];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,cofr,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|