A166592 Hankel transform of A166588(n-1).

0, 1, 3, 2, 3, 1, 0, -1, -3, -2, -3, -1, 0, 1, 3, 2, 3, 1, 0, -1, -3, -2, -3, -1, 0, 1, 3, 2, 3, 1, 0, -1, -3, -2, -3, -1, 0, 1, 3, 2, 3, 1, 0, -1, -3, -2, -3, -1, 0, 1, 3, 2, 3, 1, 0, -1, -3, -2, -3, -1, 0, 1, 3, 2, 3, 1, 0, -1, -3, -2, -3, -1, 0, 1, 3, 2, 3, 1, 0, -1, -3, -2, -3, -1, 0, 1, 3

Offset: 0

Author

Paul Barry, Oct 17 2009

Keywords

• easy
• sign

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).

Programs

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 *)

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