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

Author

Wouter Meeussen, Jan 11 2004

Keywords

• nonn

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

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..5000
• Wouter Meeussen, Mma functions for plane and solid partitions

Crossrefs

Cf. A000219, A000991, A091357.

Programs

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}]

Extensions

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

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