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A096578
Number of solid partitions with period (cycle length) two under 'time-lapse' operation.
7
0, 0, 1, 1, 1, 2, 3, 6, 7, 11, 15, 25, 33, 48, 65
OFFSET
1,6
COMMENTS
Operation 'time lapse', or 'lapse', L, operates on a solid partition by creating a new one, layer by layer. Layer k is defined by its 3-dimensional-Ferrers plot, equal to the (existence of) elements of the solid partition with value >= k. As if taking a time-lapse picture of the solid partition, filtering out elements less than k and projecting the resulting structure (filled with ones) to the base plane. Given there are three plane to project into, together with the starting solid partition, that makezs four 'isomers'.
EXAMPLE
Solid partition [{{3,1,1,1},{3}},{{2,1}},{{1}},{{1}},{{1}}] lapses (L) into
[{{4,1},{2},{1},{1},{1}},{{1,1},{1}},{{1,1}}], then into
[{{2,1,1,1,1},{2,1},{2}},{{1,1}},{{1}},{{1}}], further into
[{{5,2,1},{2},{1},{1}},{{1,1,1}}] and returns after L^4 to
[{{3,1,1,1},{3}},{{2,1}},{{1}},{{1}},{{1}}]
MATHEMATICA
See link above.
KEYWORD
more,nonn
AUTHOR
Wouter Meeussen, Jun 27 2004
STATUS
approved