A065530 If n is odd then a(n) = n, else a(n) = n*(n+2).

0, 1, 8, 3, 24, 5, 48, 7, 80, 9, 120, 11, 168, 13, 224, 15, 288, 17, 360, 19, 440, 21, 528, 23, 624, 25, 728, 27, 840, 29, 960, 31, 1088, 33, 1224, 35, 1368, 37, 1520, 39, 1680, 41, 1848, 43, 2024, 45, 2208, 47, 2400, 49, 2600, 51, 2808, 53, 3024, 55, 3248, 57

Offset: 0

Author

George E. Antoniou, Dec 02 2001

Keywords

• easy
• nonn

Comments

Order of Fibonacci group F(n+1,2) (0 means group is infinite). - N. J. A. Sloane, Dec 30 2011

References

• D. L. Johnson, Presentation of Groups, Cambridge, 1976, p. 182.
• Thomas, Richard M., The Fibonacci groups revisited, in Groups - St. Andrews 1989, Vol. 2, 445-454, London Math. Soc. Lecture Note Ser., 160, Cambridge Univ. Press, Cambridge, 1991.

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Crossrefs

A column of A202624.

Programs

Mathematica

Array[If[OddQ[#], #, #*(#+2)] &, 100, 0] (* Paolo Xausa, Feb 22 2024 *)
With[{nn=60},Riffle[Table[n(n+2),{n,0,nn,2}],Range[1,nn+1,2]]] (* or *) LinearRecurrence[{0,3,0,-3,0,1},{0,1,8,3,24,5},100] (* Harvey P. Dale, Sep 27 2024 *)

PARI

a(n) = { if (n%2, n, n*(n + 2)) } \\ Harry J. Smith, Oct 20 2009

PARI

concat(0, Vec(x*(x^4-8*x-1)/((x-1)^3*(x+1)^3) + O(x^100))) \\ Colin Barker, May 02 2015

Formula

O.g.f.: (x+8x^2-x^5)/(1-x^2)^3. - Len Smiley, Dec 04 2001

a(n) = 3*a(n-2)-3*a(n-4)+a(n-6) for n>5. - Colin Barker, May 02 2015