

A047997


Triangle of numbers a(n,k) = number of balance positions when k equal weights are placed at a ksubset of the points {n, (n1), ..., n1, 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
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OFFSET

1,3


REFERENCES

R. E. Odeh and E. J. Cockayne, Balancing weights on the integer line, J. Combin. Theory, 7 (1969), 130135.


LINKS

Table of n, a(n) for n=1..60.


FORMULA

Equivalent to number of partitions of n(2kn+1)/2 into up to n parts each no more than 2kn+1 so a(n, k)=A067059(n, n(2kn+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}]] (* JeanFrançois 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

N. J. A. Sloane


STATUS

approved



