A096578 Number of solid partitions with period (cycle length) two under 'time-lapse' operation.

0, 0, 1, 1, 1, 2, 3, 6, 7, 11, 15, 25, 33, 48, 65

Offset: 1

Author

Wouter Meeussen, Jun 27 2004

Keywords

• nonn
• more

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'.

Examples

			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}}]
		

Links

• Wouter Meeussen, Mma functions for plane and solid partitions

Crossrefs

Cf. A000293, A094504, A094508, A096272, A096573, A096574, A096575, A096576, A096577, A096579, A096580, A096581.

Programs

Mathematica

(* See link above. *)