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Search: id:A084519
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| A084519 |
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Number of indecomposable ground-state 3-ball juggling sequences of period n. |
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+0
7
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| 1, 1, 3, 13, 47, 173, 639, 2357, 8695, 32077, 118335, 436549, 1610471, 5941181, 21917583, 80856053, 298285687, 1100404333, 4059496479, 14975869477, 55247410055, 203812962077, 751885445295, 2773777080149, 10232728055191
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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This sequence counts the length n asynchronic site swaps given in A084511/A084512.
First differences of A084518. INVERTi transform of A084509. Cf. also A084529, A003319.
Equals left border 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.
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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) seems to satisfy the recurrence : a(1) = a(2) = 1, a(3) = 3 and a(n) = 3*a(n-1)+2*a(n-2)+2*a(n-3). If so, a(n) = floor(A*B^n+1/2) where B = 3.6890953... is the real positive root of x^3-3x^2-2x-2 = 0 and A = 0.0687059... is the real positive root of 118*x^3+118*x^2+35*x-3 = 0. Benoit Cloitre, Jun 14 2003. [This conjecture is established in the Chung-Graham paper.]
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MAPLE
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INVERTi([seq(A084509(n), n=1..80)]);
with(combinat); A084519 := proc(n) option remember; local c, i, k; A084509(n)-add(add(mul(A084519(i), i=c), c=composition(n, k)), k=2..n); end;
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CROSSREFS
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A145463 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 11 2008]
Sequence in context: A121136 A017943 A089930 this_sequence A122424 A027326 A108946
Adjacent sequences: A084516 A084517 A084518 this_sequence A084520 A084521 A084522
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KEYWORD
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nonn
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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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