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A089924 Number of plane partitions of n with 3 or more columns. 6
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 (list; graph; refs; listen; history; text; internal format)
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
W. Meeussen, PlanePartitions (Mathematica program, personal web site).
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
Sequence in context: A182818 A095846 A153732 * A293947 A178457 A072916
KEYWORD
nonn
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

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Last modified July 20 20:50 EDT 2024. Contains 374459 sequences. (Running on oeis4.)