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 A084509 Number of ground-state 3-ball juggling sequences of period n. 9

%I

%S 1,2,6,24,96,384,1536,6144,24576,98304,393216,1572864,6291456,

%T 25165824,100663296,402653184,1610612736,6442450944,25769803776,

%U 103079215104,412316860416,1649267441664,6597069766656,26388279066624

%N Number of ground-state 3-ball juggling sequences of period n.

%C This sequence counts the length n asynchronic site swaps given in A084501/A084502.

%C Equals row sums of triangle A145463 [From _Gary W. Adamson_, Oct 11 2008]

%D B. Polster, The Mathematics of Juggling, Springer-Verlag, 2003, p. 48.

%H Fan Chung, Ron Graham, <a href="http://www.jstor.org/stable/27642443">Primitive juggling sequences</a>, Am. Math. Monthly 115 (3) (2008) 185-19

%H <a href="/index/J#Juggling">Index entries for sequences related to juggling</a>

%F a(n) = n! for n <= 4, a(n) = 6*4^(n-3) = A002023(n-3) for n >= 3.

%F G.f. : x(1-2x-2x^2)/(1-4x) . - _Philippe DELEHAM_, Aug 16 2005

%p A084509 := n -> `if`((n<4),n!,6*(4^(n-3)));

%p INVERT([seq(A084519(n),n=1..12)]);

%p with(finance):seq(ceil(futurevalue(6,3,n)), n=-2..21);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2009]

%Y First differences of A084508. INVERT transform of A084519. Cf. also A084529.

%Y A145463 [From _Gary W. Adamson_, Oct 11 2008]

%K nonn,easy

%O 1,2

%A _Antti Karttunen_ Jun 02 2003

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Last modified May 21 06:51 EDT 2013. Contains 225477 sequences.