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Search: id:A084509
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| A084509 |
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Number of ground-state 3-ball juggling sequences of period n. |
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+0
9
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| 1, 2, 6, 24, 96, 384, 1536, 6144, 24576, 98304, 393216, 1572864, 6291456, 25165824, 100663296, 402653184, 1610612736, 6442450944, 25769803776, 103079215104, 412316860416, 1649267441664, 6597069766656, 26388279066624
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This sequence counts the length n asynchronic site swaps given in A084501/A084502.
Equals row sums of triangle A145463 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 11 2008]
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REFERENCES
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F. R. K. Chung and R. L. Graham, Primitive juggling sequences, preprint, 2006.
B. Polster, The Mathematics of Juggling, Springer-Verlag, 2003, p. 48.
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LINKS
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Index entries for sequences related to juggling
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FORMULA
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a(n) = n! for n <= 4, a(n) = 6*4^(n-3) = A002023(n-3) for n >= 3.
G.f. : x(1-2x-2x^2)/(1-4x) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 16 2005
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MAPLE
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A084509 := n -> `if`((n<4), n!, 6*(4^(n-3)));
INVERT([seq(A084519(n), n=1..12)]);
with(finance):seq(ceil(futurevalue(6, 3, n)), n=-2..21); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2009]
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CROSSREFS
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First differences of A084508. INVERT transform of A084519. Cf. also A084529.
A145463 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 11 2008]
Sequence in context: A147930 A147918 A072855 this_sequence A147915 A147906 A147898
Adjacent sequences: A084506 A084507 A084508 this_sequence A084510 A084511 A084512
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KEYWORD
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nonn,easy
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AUTHOR
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Antti Karttunen (my_firstname.my_surname(AT)iki.fi) Jun 02 2003
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