OFFSET
0,3
COMMENTS
Hankel transform of 0,1,2,2,3,3,5,5,10,10,... is -a(n).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..100
Index entries for linear recurrences with constant coefficients, signature (0,1,0,-1).
FORMULA
G.f.: x(1+3x+x^2)/(1-x^2+x^4).
a(n) = (1-sqrt(3))*sin(5*Pi*n/6)+(1+sqrt(3))*sin(Pi*n/6).
From G. C. Greubel, May 18 2016: (Start)
a(n+12) = a(n).
a(n) = a(n-2) - a(n-4). (End)
E.g.f.: 2*sin(x/2)*(sqrt(3)*sinh(sqrt(3)*x/2) + cosh(sqrt(3)*x/2)). - Ilya Gutkovskiy, May 18 2016
MATHEMATICA
CoefficientList[Series[x (1 + 3 x + x^2)/(1 - x^2 + x^4), {x, 0, 10}], x] (* or *) LinearRecurrence[{0, 1, 0, -1}, {0, 1, 3, 2}, 25] (* G. C. Greubel, May 18 2016 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Oct 17 2009
STATUS
approved