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A078684 a(n) = 3^floor(n^2/4). 0
1, 1, 3, 9, 81, 729, 19683, 531441, 43046721, 3486784401, 847288609443, 205891132094649, 150094635296999121, 109418989131512359209, 239299329230617529590083, 523347633027360537213511521, 3433683820292512484657849089281, 22528399544939174411840147874772641 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of groves of order n.

LINKS

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

Gabriel D. Carroll and David Speyer, The cube recurrence

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

MATHEMATICA

Table[3^Floor[n^2/4], {n, 0, 20}] (* Harvey P. Dale, May 08 2011 *)

PROG

(PARI) {a(n) = 3^(n^2\4)} /* Michael Somos, Sep 16 2005 */

CROSSREFS

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

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Last modified June 15 22:19 EDT 2019. Contains 324145 sequences. (Running on oeis4.)