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Search: id:A047997
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| A047997 |
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Triangle of numbers a(n,k) = number of balance positions when k equal weights are placed at a k-subset of the points {-n, -(n-1), ..., n-1, n} on a centrally pivoted rod. |
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+0
3
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| 1, 1, 2, 1, 3, 5, 1, 4, 8, 12, 1, 5, 13, 24, 32, 1, 6, 18, 43, 73, 94, 1, 7, 25, 69, 141, 227, 289, 1, 8, 32, 104, 252, 480, 734, 910, 1, 9, 41, 150, 414, 920, 1656, 2430, 2934, 1, 10, 50, 207, 649, 1636, 3370, 5744, 8150, 9686, 1, 11, 61, 277, 967
(list; table; graph; listen)
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OFFSET
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1,3
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REFERENCES
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R. E. Odeh and E. J. Cockayne, Balancing weights on the integer line, J. Combin. Theory, 7 (1969), 130-135.
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FORMULA
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Equivalent to number of partitions of n(2k-n+1)/2 into up to n parts each no more than 2k-n+1 so a(n, k)=A067059(n, n(2k-n+1)/2); row sums are A047653(n)-1. - Henry Bottomley (se16(AT)btinternet.com), Aug 11 2001
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CROSSREFS
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a(n, n) is A002838.
Adjacent sequences: A047994 A047995 A047996 this_sequence A047998 A047999 A048000
Sequence in context: A119355 A076110 A117584 this_sequence A049069 A030237 A118243
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KEYWORD
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nonn,nice,tabl
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AUTHOR
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njas
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