OFFSET
0,5
COMMENTS
Binomial transform of A105367.
LINKS
FORMULA
G.f.: (1-2x+2x^2-x^3)/(1-3x+4x^2-2x^3+x^4).
a(n) = 3*a(n-1)-4*a(n-2)+2*a(n-3)-a(n-4).
a(n) = (1/2+sqrt(5)/2)^n((1/2+sqrt(5)/10)cos(Pi*n/5)+sqrt(1/10-sqrt(5)/50)sin(Pi*n/5))- (sqrt(5)/2-1/2)^n((sqrt(5)/10-1/2)cos(2*Pi*n/5)+sqrt(1/10+sqrt(5)/50)sin(2*Pi*n/5)).
a(5n) = -F(-5n-1), a(5n+1) = a(5n+2) = -F(-5n-2), a(5n+3) = 0, a(5n+4) = F(-5n-4). - Michael Somos, Apr 09 2005
MATHEMATICA
CoefficientList[Series[(1-x)(1-x+x^2)/(1-3x+4x^2-2x^3+x^4), {x, 0, 60}], x] (* or *) LinearRecurrence[{3, -4, 2, -1}, {1, 1, 1, 0}, 60] (* Harvey P. Dale, Dec 21 2013 *)
PROG
(PARI) a(n)=local(m); m=n%5+1; [1, -1, -1, 0, 1][m]*fibonacci(-n-(m<3)) /* Michael Somos, Apr 09 2005 */
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Apr 01 2005
STATUS
approved