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A048140
Number of planar partitions of n, but partitions that are mirror images of each other (when regarded as 3-D objects) are counted only once.
5
1, 2, 4, 8, 14, 27, 47, 86, 149, 261, 444, 760, 1269, 2119, 3486, 5711, 9247, 14906, 23800, 37816, 59622, 93528, 145759, 226071, 348612, 535131, 817280, 1242824, 1881310, 2836377, 4258509, 6369669, 9491142, 14092537, 20851146, 30749471
OFFSET
1,2
COMMENTS
Plane partitions seen as 3-dimensional-objects can have a mirror symmetry plane.
LINKS
Jean-François Alcover, Table of n, a(n) for n = 1..1000
EXAMPLE
n=3 gives 4 forms: {{3}}; {{1,1,1}}={{1},{1},{1}}; {{2,1}}={{2},{1}}; {{1,1},{1}}.
MATHEMATICA
terms = 100;
a219[0] = 1;
a219[n_] := a219[n] = Sum[a219[n - j] DivisorSigma[2, j], {j, n}]/n;
s = Product[1/(1 - x^(2i - 1))/(1 - x^(2i))^Floor[i/2], {i, 1, Ceiling[ (terms+1)/2]}] + O[x]^(terms+1);
A005987 = CoefficientList[s, x];
a[n_] := (a219[n] + A005987[[n+1]])/2;
a /@ Range[terms] (* Jean-François Alcover, Dec 28 2019 *)
CROSSREFS
Equals (A000219+A005987)/2.
Equals 2 Cs + 3 C1 + C3 + C3v, Cs=A000784, C1=A000785, C3=A048142, C3v=A048141. Cf. A000219, A005987.
Sequence in context: A164161 A068011 A048238 * A179817 A214255 A065616
KEYWORD
nonn
EXTENSIONS
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 08 2007
STATUS
approved