A258421 Number of partitions of the 7-dimensional hypercube resulting from a sequence of n bisections, each of which splits any part perpendicular to any of the axes, such that each axis is used at least once.

2162160, 196756560, 10778727960, 463305056760, 17266750912320, 586609859314080, 18699578507549520, 569565504689176800, 16777853060738524020, 482011338862966969980, 13586929812483090607600, 377442353035435719228120, 10367784656620152180344310

Offset

7,1

Links

Alois P. Heinz, Table of n, a(n) for n = 7..700

Maple

b:= proc(n, k, t) option remember; `if`(t=0, 1, `if`(t=1,
       A(n-1, k), add(A(j, k)*b(n-j-1, k, t-1), j=0..n-2)))
    end:
A:= proc(n, k) option remember; `if`(n=0, 1,
      -add(binomial(k, j)*(-1)^j*b(n+1, k, 2^j), j=1..k))
    end:
T:= proc(n, k) option remember;
      add(A(n, k-i)*(-1)^i*binomial(k, i), i=0..k)
    end:
a:= n-> T(n, 7):
seq(a(n), n=7..25);

Crossrefs

Column k=7 of A255982.

Sequence in context: A253966 A253762 A154874 * A166930 A183754 A049359

Adjacent sequences: A258418 A258419 A258420 * A258422 A258423 A258424

Keyword

nonn

Author

Alois P. Heinz, May 29 2015

Status

approved