%I A096573
%S A096573 1,2,4,8,13,24,39,68,110,182,288,468,728,1150,1770
%N A096573 Number of fixed points of mirroring operation on solid partitions.
%C A096573 Uses function "solidformBTK" from link above.
%H A096573 Wouter Meeussen, <a href="http://users.pandora.be/Wouter.Meeussen/SolidPartitions.txt">
               Solid Partitions Mathematica functions</a>
%e A096573 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.
%t A096573 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}]
%Y A096573 Cf. A000293, A094504, A094508, A096272, A096574, A096575, A096576, A096577, 
               A096578, A096579, A096580, A096581.
%Y A096573 Sequence in context: A023600 A074467 A018066 this_sequence A000077 A054164 
               A102704
%Y A096573 Adjacent sequences: A096570 A096571 A096572 this_sequence A096574 A096575 
               A096576
%K A096573 more,nonn
%O A096573 1,2
%A A096573 Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jun 27 2004