A237025 Number of partitions of the 10-dimensional hypercube resulting from a sequence of n bisections, each of which splits any part perpendicular to any of the axes.

1, 10, 200, 4955, 137300, 4074000, 126608100, 4068161370, 134057837000, 4505692837250, 153860041920200, 5322981634672000, 186175022952887500, 6572164280362285000, 233857080811291255200, 8379031938022660903665, 302042773405644342524700

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..10} (-1)^i*C(10,i)*(G*x)^(2^(10-i)).

Crossrefs

Column k=10 of A237018.

Sequence in context: A335649 A202436 A320671 * A156275 A036362 A051262

Adjacent sequences: A237022 A237023 A237024 * A237026 A237027 A237028

Keyword

nonn

Author

Alois P. Heinz, Feb 02 2014

Status

approved