OFFSET
0,3
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).
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
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 *)
PROG
(PARI) { for (n=0, 1000, if (n%2, a=n, a=n*(n + 2)); write("b065530.txt", n, " ", a) ) } \\ 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
CROSSREFS
KEYWORD
easy,nonn,changed
AUTHOR
George E. Antoniou, Dec 02 2001
STATUS
approved