A237023 Number of partitions of the 8-dimensional hypercube resulting from a sequence of n bisections, each of which splits any part perpendicular to any of the axes.

1, 8, 128, 2532, 56000, 1326080, 32885824, 843189944, 22171138432, 594590989696, 16200867745408, 447218004699648, 12480580062841856, 351535051446944768, 9980583165975732736, 285327120847367853498, 8206545372905533247648, 237302661850471880634624

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..8} (-1)^i*C(8,i)*(G*x)^(2^(8-i)).

Crossrefs

Column k=8 of A237018.

Sequence in context: A013777 A183497 A370102 * A156270 A051189 A371299

Adjacent sequences: A237020 A237021 A237022 * A237024 A237025 A237026

Keyword

nonn

Author

Alois P. Heinz, Feb 02 2014

Status

approved