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Search: id:A137268
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| A137268 |
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Period and balls triangular sequence for Juggling from Chung-Graham. |
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+0
1
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| 1, 2, 2, 4, 6, 6, 8, 18, 24, 24, 16, 54, 96, 120, 120, 32, 162, 384, 600, 720, 720, 64, 486, 1536, 3000, 4320, 5040, 5040, 128, 1458, 6144, 15000, 25920, 35280, 40320, 40320, 256, 4374, 24576, 75000, 155520, 246960, 322560, 362880, 362880, 512, 13122
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sum sequence is:
{1, 4, 16, 74, 406, 2618, 19486, 164570, 1555006, 16252778}
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REFERENCES
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http://www.maa.org/pubs/monthly_mar08_toc.html; Primitive Juggling Sequences; By: Fan Chung and Ron Graham; fan(AT)ucsd.edu, graham(AT)ucsd.edu; page 188
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FORMULA
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using their notation: J(b,n)=If[ n ≁ b, (b + 1)^(n - b)*b!, n! ]
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EXAMPLE
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{1},
{2, 2},
{4, 6, 6},
{8, 18, 24, 24},
{16, 54, 96, 120, 120},
{32, 162, 384, 600, 720, 720},
{64, 486, 1536, 3000, 4320, 5040, 5040},
{128, 1458, 6144, 15000, 25920,35280, 40320, 40320},
{256, 4374, 24576, 75000, 155520,246960, 322560, 362880, 362880},
{512, 13122, 98304, 375000, 933120, 1728720, 2580480, 3265920, 3628800, 3628800}
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MATHEMATICA
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J[b_, n_] = If[ n ≁ b, (b + 1)^(n - b)*b!, n! ]; c = Table[Table[J[b, n], {b, 1, n}], {n, 1, 10}]; Flatten[c]
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CROSSREFS
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Adjacent sequences: A137265 A137266 A137267 this_sequence A137269 A137270 A137271
Sequence in context: A109832 A039731 A005341 this_sequence A008130 A055388 A065457
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 12 2008
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