A237020 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.

1, 5, 50, 615, 8450, 124250, 1912900, 30444385, 496856750, 8269863250, 139842071300, 2395663877750, 41489577762500, 725209189182500, 12777189397865800, 226674511923129620, 4045726807789468300, 72595935311731692500, 1308866748433105251000

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..5} (-1)^i*C(5,i)*(G*x)^(2^(5-i)).

Crossrefs

Column k=5 of A237018.

Sequence in context: A199762 A078244 A233068 * A156058 A232997 A357405

Adjacent sequences: A237017 A237018 A237019 * A237021 A237022 A237023

Keyword

nonn

Author

Alois P. Heinz, Feb 02 2014

Status

approved