|
Search: id:A014292
|
|
|
| A014292 |
|
a(0) = a(1) = 0, a(2) = 1, a(3) = 2; for n >= 4, a(n)=2*a(n-1)-a(n-2)-a(n-4). |
|
+0
4
|
|
| 0, 0, 1, 2, 3, 4, 4, 2, -3, -12, -25, -40, -52, -52, -27, 38, 155, 324, 520, 678, 681, 360, -481, -2000, -4200, -6760, -8839, -8918, -4797, 6084, 25804, 54442, 87877, 115228, 116775, 63880, -76892, -332892, -705667, -1142322
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
Imaginary part of the sequence of complex numbers defined by c(0) = 1, c(1) = 1, for n>1 c(n) = c(n-1) + i*c(n-2). - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Apr 24 2005
a(n) = sqrt(3)*y where (x,y,y,y) is the quaternion b(n) of the sequence b of quaternions defined by b(0)=1,b(1)=1, b(n) = b(n-1) + b(n-2)*(0,s,s,s) where s = 1/sqrt(3). - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Apr 25 2005
|
|
FORMULA
|
a(n)=sum{k=0..floor((n+2)/2), C(n-k+2, k)sin(pi*k/2)}. - Paul Barry (pbarry(AT)wit.ie), Apr 25 2005
G.f.: x^2/(1-2x+x^2+x^4). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 22 2008]
|
|
CROSSREFS
|
Cf. A104862, A104862.
Sequence in context: A134581 A099587 A160386 this_sequence A066078 A058339 A133852
Adjacent sequences: A014289 A014290 A014291 this_sequence A014293 A014294 A014295
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
Search completed in 0.005 seconds
|
