A237021 Number of partitions of the 6-dimensional hypercube resulting from a sequence of n bisections, each of which splits any part perpendicular to any of the axes.

1, 6, 72, 1065, 17604, 311472, 5770692, 110530514, 2171011800, 43490709702, 885138113016, 18250712631216, 380432844142092, 8003697071972760, 169728054535951520, 3624215619984643650, 77857888349211858000, 1681568232191988128040, 36491768084579204728800

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..300

Yu Hin (Gary) Au, Fatemeh Bagherzadeh, Murray R. Bremner, Enumeration and Asymptotic Formulas for Rectangular Partitions of the Hypercube, arXiv:1903.00813 [math.CO], Mar 03 2019.

Formula

G.f. G satisfies: x = Sum_{i=0..6} (-1)^i*C(6,i)*(G*x)^(2^(6-i)).

Crossrefs

Column k=6 of A237018.

Sequence in context: A370098 A303342 A332705 * A156128 A052678 A052719

Adjacent sequences: A237018 A237019 A237020 * A237022 A237023 A237024

Keyword

nonn

Author

Alois P. Heinz, Feb 02 2014

Status

approved