|
Search: id:A096597
|
|
|
| A096597 |
|
Triangle read by rows: T[n,m] = number of plane partitions of n whose 3-dimensional Ferrers plot just fits inside an m X m X m box. Equivalently, with Max[parts, rows, columns] = m. |
|
+0
2
|
|
| 1, 0, 3, 0, 3, 3, 0, 4, 6, 3, 0, 3, 12, 6, 3, 0, 3, 21, 15, 6, 3, 0, 1, 31, 30, 15, 6, 3, 0, 1, 42, 60, 33, 15, 6, 3, 0, 0, 54, 102, 69, 33, 15, 6, 3, 0, 0, 64, 175, 132, 72, 33, 15, 6, 3, 0, 0, 73, 270, 246, 141, 72, 33, 15, 6, 3, 0, 0, 81, 417, 432, 276, 144, 72, 33, 15, 6, 3, 0, 0, 83
(list; table; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Row sums equal A000219 (plane partitions). Table starts 1; 0,3; 0,3,3; 0,4,6,3; 0,3,12,6,3; ... Conjecture: the last (Floor[n/2]) terms of each row read backwards are 3* A091360 (running sum of A000219).
|
|
LINKS
|
George E. Andrews, On a Partition Function of Richard Stanley.
|
|
FORMULA
|
k-th column is CoefficientList[Series[qMacMahon[k]-qMacMahon[k-1], {q, 0, 3^k}], q] with qMacMahon[n_Integer]:=Product[qan[i+j+k-1]/qan[i+j+k-2], {i, n}, {j, n}, {k, n}] and qan[n_]:=(q^n-1)/(q-1) - Wouter Meeussen (wouter.meeussen(AT)pandora.be), Aug 28 2004
|
|
EXAMPLE
|
T[5,2]=3 represents the plane partitions {{2,1},{2}}, {{2,1},{1,1}} and {{2,2},{1}}.
|
|
MATHEMATICA
|
(* see A089924 for "planepartitions[]" *) Table[Rest@CoefficientList[Plus@@(x ^ Max[Flatten[ # ], Length[ # ], Max[Length/@# ]]&/@ planepartitions[n]), x], {n, 19}]
|
|
CROSSREFS
|
Cf. A096272, A091360.
Sequence in context: A112470 A115379 A127801 this_sequence A097994 A053604 A066958
Adjacent sequences: A096594 A096595 A096596 this_sequence A096598 A096599 A096600
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Wouter Meeussen (wouter.meeussen(AT)pandora.be), Aug 14 2004
|
|
|
Search completed in 0.002 seconds
|
