OFFSET
0,3
COMMENTS
Number of groves of order n.
Tropical version is sequence A002620. - Michael Somos, Mar 14 2020
LINKS
Gabriel D. Carroll and David Speyer, The cube recurrence, The Electronic Journal of Combinatorics, Volume 11, Issue 1 (2004), R73.
FORMULA
a(n) = 9*a(n-2)^2/a(n-4). - Michael Somos, Sep 16 2005
0 = a(n)*a(n+3) - 3*a(n+1)*a(n+2) for all n in Z. - Michael Somos, Jan 25 2014
a(n) = a(-n) for all n in Z. a(n) = 3^A002620(n). - Michael Somos, Mar 14 2020
MATHEMATICA
Table[3^Floor[n^2/4], {n, 0, 20}] (* Harvey P. Dale, May 08 2011 *)
a[ n_] := 3^Quotient[n^2, 4]; (* Michael Somos, Mar 14 2020 *)
PROG
(PARI) {a(n) = 3^(n^2\4)} /* Michael Somos, Sep 16 2005 */
(Magma) [3^Floor(n^2/4): n in [0..20]]; // Vincenzo Librandi, Mar 17 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 18 2002
STATUS
approved