A242409 Number of plane partitions of n into parts which decrease by 1 along each row and column.

1, 1, 1, 3, 2, 3, 3, 4, 4, 8, 5, 3, 6, 6, 6, 13, 9, 7, 13, 13, 7, 13, 9, 8, 19, 13, 11, 22, 17, 22, 27, 19, 20, 33, 26, 14, 24, 19, 16, 38, 26, 17, 42, 35, 36, 60, 34, 38, 56, 56, 55, 56, 60, 42, 67, 46, 31, 57, 52, 62, 52, 65, 48, 86, 99, 50, 95, 78, 77, 128, 104, 90, 142, 127, 114, 161, 110, 113, 184, 155, 122

Offset

0,4

Links

Table of n, a(n) for n=0..80.

Example

For n=8 the four plane partitions which are counted are: ((8)),((3,2,1),(2)), ((3,2),(2,1)), ((3,2),(2),(1)).

Mathematica

<<Combinatorica`
gf=1;
For[n=1, n<=25, n++,
unre=Partitions[n];
For[m=1, m<=Length[unre], m++,
For[i=1, i<=n, i++,
For[j=1, j<=n, j++, box[i, j]=0]];
For[i=1, i<=Length[unre[[m]]], i++,
For[j=1, j<=unre[[m]][[i]], j++, box[i, j]=i+j-1]];
max=Max[Table[box[i, j], {i, 1, n}, {j, 1, n}]];
For[i=1, i<=Length[unre[[m]]], i++,
For[j=1, j<=unre[[m]][[i]], j++, box[i, j]=max+1-box[i, j]]];
sum=0;
For[i=1, i<=Length[unre[[m]]], i++,
For[j=1, j<=unre[[m]][[i]], j++, sum=sum+box[i, j]]];
function=x^sum/(1-x^n);
gf=gf+function]];
CoefficientList[Series[gf, {x, 0, 80}], x]

Crossrefs

Sequence in context: A061266 A345755 A111114 * A317623 A286244 A230010

Adjacent sequences: A242406 A242407 A242408 * A242410 A242411 A242412

Keyword

nonn

Author

David S. Newman, May 13 2014

Status

approved