A089924 Number of plane partitions of n with 3 or more columns.

0, 0, 1, 3, 8, 19, 41, 85, 167, 319, 588, 1066, 1880, 3272, 5588, 9431, 15686, 25841, 42070, 67926, 108634, 172467, 271643, 425109, 660756, 1021170, 1568905, 2398059, 3646437, 5519025, 8314623, 12473538, 18634748, 27731820, 41113453, 60735830, 89411503, 131193675

Offset

1,4

Comments

Because of symmetry of the 3-dimensional-Ferrers plots, this sequence also counts the plane partitions with 3 or more rows and the plane partitions with maximal element >= 3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..5000

Wouter Meeussen, Mma functions for plane and solid partitions

Example

a(4)=3:
  1111 111 211
  .... 1.. ...

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, add(add(min(d, k)
      *d, d=numtheory[divisors](j))*b(n-j, k), j=1..n)/n)
    end:
a:= n-> b(n, infinity)-b(n, 2):
seq(a(n), n=1..50);  # Alois P. Heinz, Sep 24 2018

Mathematica

(* planepartitions[] : see link *); Table[Count[planepartitions[n], q_ /; Length[First[q]] >= 3], {n, 12}]

Crossrefs

Cf. A000219, A000991, A091357.

Sequence in context: A182818 A095846 A153732 * A293947 A178457 A072916

Adjacent sequences: A089921 A089922 A089923 * A089925 A089926 A089927

Keyword

nonn,changed

Author

Wouter Meeussen, Jan 11 2004

Extensions

a(21)-a(27) from Vaclav Kotesovec, May 05 2018

a(28)-a(38) from Alois P. Heinz, Sep 24 2018

Status

approved