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Plane partitions into odd parts.
0

%I #24 May 06 2018 03:12:39

%S 1,1,2,4,7,11,20,30,50,75,121,176,276,398,604,864,1285,1814,2652,3713,

%T 5339,7417,10526,14500,20349,27836,38653,52528,72291,97612,133249,

%U 178889,242379,323634,435557,578579,773877,1023074,1360565

%N Plane partitions into odd parts.

%e Example for n=4:

%e ((3,1)), ((3)(1)), ((1,1,1,1)), ((1,1,1),(1)),

%e ((1,1),(1,1)), ((1,1),(1),(1)), ((1),(1),(1),(1)).

%t << Combinatorica`

%t pilings[par_List]:=Module[{tel,alles},tel=Length[par];alles=List/@Partitions[par[[1]]];

%t Do[alles=Flatten[Function[argu,(Flatten[{argu,{#1}},1]&)/@Select[Partitions[par[[i]]],Length[#1]<=Length[Last[argu]]&&And@@Thread[#1<=Take[Last[argu],Length[#1]]]&]]/@alles,1],{i,2,tel}];alles];

%t Table[Tr[Count[pilings[#],q_/;FreeQ[q,_?EvenQ]]&/@Partitions[w]],{w,24}]

%Y Cf. A000219.

%K nonn

%O 0,3

%A _David S. Newman_, May 11 2014

%E a(8)-a(24) from _Wouter Meeussen_

%E a(25)-a(38) from _Vaclav Kotesovec_, May 05 2018