A096573 Number of fixed points of mirroring operation on solid partitions.

1, 2, 4, 8, 13, 24, 39, 68, 110, 182, 288, 468, 728, 1150, 1770

Offset

1,2

Comments

Uses function "solidformBTK" from link above.

Links

Table of n, a(n) for n=1..15.

Wouter Meeussen, Solid Partitions Mathematica functions

Luigi Togliani, Forms of Crossed and Simple Polygons, Science & Philosophy (2019) Vol. 7, No. 2, 71-82.

Example

Solid partition [{{3, 1, 1, 1}, {3}}, {{2, 1}}, {{1}}, {{1}}, {{1}}] mirrors into [{{3, 3}, {1}, {1}, {1}}, {{2}, {1}}, {{1}}, {{1}}, {{1}}] by mirroring each layer as a plane partition.

Mathematica

flip[pili_List] := Module[{wide, it}, wide =Length[pili[[1]]]; it = Join[ #, Table[0, {wide - Length[ # ]}]] & /@ pili; DeleteCases[ Transpose[it], 0 | {}, -1]]; Table[sn = Sort@Flatten[solidformBTK /@ Partitions[n]]; Frequencies[Length /@ ToCycles[Ordering[Map[flip@ # &, sn, {2}]]] ], {n, 1, 15}]

Crossrefs

Cf. A000293, A094504, A094508, A096272, A096574, A096575, A096576, A096577, A096578, A096579, A096580, A096581.

Sequence in context: A227232 A164408 A303852 * A348574 A227910 A000077

Adjacent sequences: A096570 A096571 A096572 * A096574 A096575 A096576

Keyword

nonn,more

Author

Wouter Meeussen, Jun 27 2004

Status

approved