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A095988
Number of Gray codes for partitions of n.
0
1, 1, 1, 1, 3, 1, 52, 652, 298896, 2291100484
OFFSET
1,5
COMMENTS
List the partitions of n and form a graph where two partitions are connected if one can be transformed into the other by adding 1 from one element, subtracting 1 from another element and rearranging (if necessary). A Gray code corresponds to a Hamiltonian path through all of the partitions.
Terms a(6) through a(10) are given in the Knuth reference.
REFERENCES
D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, (to appear), section 7.2.1.4.
EXAMPLE
The partitions of the integer 6 are 111111, 21111, 3111, 2211, 222, 321, 33, 42, 411, 51, 6. Each term is obtained from the previous term by adding 1 to one element, subtracting 1 from another element and rearranging. This is the only way to do it for 6, so a(6)=1.
CROSSREFS
Sequence in context: A133104 A322730 A292425 * A189898 A082525 A162221
KEYWORD
hard,nonn
AUTHOR
Jud McCranie, Jul 18 2004
STATUS
approved