A258419 Number of partitions of the 5-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.

5040, 230400, 6792750, 165293700, 3624918660, 74699100720, 1479942440340, 28577108044800, 542482698531000, 10181610525525360, 189663357076785270, 3515970161266821510, 64985380300281057950, 1199146771516702098500, 22111945264260791498090

Offset

5,1

Links

Alois P. Heinz, Table of n, a(n) for n = 5..750

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, 5):
seq(a(n), n=5..25);

Mathematica

b[n_, k_, t_] := b[n, k, t] = If[t == 0, 1, If[t == 1, A[n - 1, k], Sum[A[j, k]*b[n - j - 1, k, t - 1], {j, 0, n - 2}]]];
A[n_, k_] := A[n, k] = If[n == 0, 1, -Sum[Binomial[k, j]*(-1)^j*b[n + 1, k, 2^j], {j, 1, k}]];
T[n_, k_] := Sum[A[n, k - i]*(-1)^i*Binomial[k, i], {i, 0, k}];
a[n_] := T[n, 5];
a /@ Range[5, 25] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)

Crossrefs

Column k=5 of A255982.

Sequence in context: A135456 A254080 A228910 * A355023 A179062 A342075

Adjacent sequences: A258416 A258417 A258418 * A258420 A258421 A258422

Keyword

nonn

Author

Alois P. Heinz, May 29 2015

Status

approved