|
|
A078069
|
|
Expansion of (1-x)/(1+2*x+2*x^2).
|
|
6
|
|
|
1, -3, 4, -2, -4, 12, -16, 8, 16, -48, 64, -32, -64, 192, -256, 128, 256, -768, 1024, -512, -1024, 3072, -4096, 2048, 4096, -12288, 16384, -8192, -16384, 49152, -65536, 32768, 65536, -196608, 262144, -131072, -262144, 786432, -1048576, 524288, 1048576, -3145728, 4194304, -2097152, -4194304
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Pisano period lengths: 1, 1, 8, 1, 4, 8, 24, 1, 24, 4, 40, 8, 12, 24, 8, 1, 16, 24, 72, 4,... - R. J. Mathar, Aug 10 2012
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (-2)*(a(n-1)+a(n-2)), n>1 ; a(0)=1, a(1)=-3. - Philippe Deléham, Nov 19 2008
G.f.: G(0)*(1 - x)/(2*(1 + x)), where G(k)= 1 + 1/(1 - x*(k+1)/(x*(k+2) - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 20 2013
a(n) = (1/2 - I)*(-1 - I)^n + (1/2 + I)*(-1 + I)^n, n>=0. Taras Goy, Apr 20 2019
|
|
MATHEMATICA
|
CoefficientList[Series[(1-x)/(1+2x+2x^2), {x, 0, 50}], x] (* or *) LinearRecurrence[{-2, -2}, {1, -3}, 50] (* Harvey P. Dale, Jan 19 2012 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|