A078684 a(n) = 3^floor(n^2/4).

1, 1, 3, 9, 81, 729, 19683, 531441, 43046721, 3486784401, 847288609443, 205891132094649, 150094635296999121, 109418989131512359209, 239299329230617529590083, 523347633027360537213511521, 3433683820292512484657849089281, 22528399544939174411840147874772641

Offset

0,3

Comments

Number of groves of order n.

Tropical version is sequence A002620. - Michael Somos, Mar 14 2020

Links

Table of n, a(n) for n=0..17.

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

Cf. A002620.

Sequence in context: A171557 A055156 A047912 * A121858 A215114 A032108

Adjacent sequences: A078681 A078682 A078683 * A078685 A078686 A078687

Keyword

nonn

Author

N. J. A. Sloane, Dec 18 2002

Status

approved