A258422 Number of partitions of the 8-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.

57657600, 6895848960, 485566099200, 26364414061440, 1224007231940640, 51216101151626880, 1991943704397427200, 73440737647137519120, 2601107886874207253760, 89332305977055996111040, 2995343867463073686769440, 98555316817167057069129600

Offset

8,1

Links

Alois P. Heinz, Table of n, a(n) for n = 8..650

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, 8):
seq(a(n), n=8..25);

Crossrefs

Column k=8 of A255982.

Sequence in context: A269476 A234759 A172593 * A172679 A034612 A015355

Adjacent sequences: A258419 A258420 A258421 * A258423 A258424 A258425

Keyword

nonn

Author

Alois P. Heinz, May 29 2015

Status

approved