VOOZH about

URL: https://oeis.org/A242409

⇱ A242409 - OEIS

login
A242409
Number of plane partitions of n into parts which decrease by 1 along each row and column.
0
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
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
KEYWORD
nonn
AUTHOR
David S. Newman, May 13 2014
STATUS
approved