1,5

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.

D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, (to appear), section 7.2.1.4.

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.

Sequence in context: A098341 A010292 A133104 this_sequence A082525 A016482 A071291

Adjacent sequences: A095985 A095986 A095987 this_sequence A095989 A095990 A095991

hard,nonn

Jud McCranie (j.mccranie(AT)comcast.net), Jul 18 2004