A258418 Number of partitions of the 4-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.

336, 9744, 192984, 3279060, 51622600, 779602164, 11499880768, 167393051696, 2419080596520, 34838703973728, 501182126787744, 7212689238965297, 103937431212291680, 1500609318117978064, 21713411768745550544, 314940143510352714144, 4579270473409470432352

Offset: 4

Author

Alois P. Heinz, May 29 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..800

Crossrefs

Column k=4 of A255982.

Programs

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, 4):
seq(a(n), n=4..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, 4];
a /@ Range[4, 25] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)