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 A047997 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. 3
 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; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES R. E. Odeh and E. J. Cockayne, Balancing weights on the integer line, J. Combin. Theory, 7 (1969), 130-135. LINKS FORMULA 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 = A212352(n). - Henry Bottomley, Aug 11 2001 MATHEMATICA a[n_, k_] := Length[ IntegerPartitions[ n*(2k - n + 1)/2, n, Range[2k - n + 1]]]; Flatten[ Table[ a[n, k], {k, 1, 11}, {n, 1, k}]] (* Jean-François Alcover, Jan 02 2012 *) CROSSREFS a(n, n) is A002838. Cf. A047653, A212353. Sequence in context: A076110 A117584 A199847 * A188211 A175009 A297395 Adjacent sequences:  A047994 A047995 A047996 * A047998 A047999 A048000 KEYWORD nonn,nice,tabl AUTHOR STATUS approved

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Last modified December 11 07:47 EST 2019. Contains 329914 sequences. (Running on oeis4.)