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A236691 Number of totally symmetric solid partitions which fit in an n X n X n X n box. 0
1, 2, 6, 32, 352, 9304, 683464, 161960220 (list; graph; refs; listen; history; text; internal format)



Also, for n>0, the number of totally symmetric (n-1)-dimensional partitions which fit in an (n-1)-dimensional box whose sides all have length 5.

There is no conjectured formula for a(n).

The formula a(n,d)=product{i_1=1..n, product{i_2=i_1..n, .. product{i_d=i_(d-1)..n, (i_1+i_2+..i_d-d+2)/(i_1+i_2+..i_d-d+1)}}..} gives the number of totally symmetric d-dimensional partitions that fit in a box whose sides all have length n, for d=1,2, and 3.  For d>3 this formula fails. In particular, when d=4 it produces the sequence: 1, 2, 6, 32, 352, 9216, 661504... rather than the sequence above.


Table of n, a(n) for n=0..7.


This is the 4-dimensional case. Dimensions 1, 2, and 3 are respectively given by: A000027, A000079, and A005157.

Cf. A097516.

Sequence in context: A272661 A005742 A055612 * A056642 A001199 A232469

Adjacent sequences:  A236688 A236689 A236690 * A236692 A236693 A236694




Graham H. Hawkes, Jan 30 2014



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Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)