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

4,1

Links

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

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 *)

Crossrefs

Column k=4 of A255982.

Sequence in context: A223446 A229697 A268626 * A268969 A056933 A289346

Adjacent sequences: A258415 A258416 A258417 * A258419 A258420 A258421

Keyword

nonn

Author

Alois P. Heinz, May 29 2015

Status

approved