A237024 Number of partitions of the 9-dimensional hypercube resulting from a sequence of n bisections, each of which splits any part perpendicular to any of the axes.

1, 9, 162, 3609, 89910, 2398410, 67006116, 1935501645, 57335681142, 1732321234710, 53177078182860, 1653802745967450, 51997089469768380, 1650038052325122324, 52779255878344803336, 1699938398827907195607, 55085070458854388052090, 1794568569427662345343962

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..9} (-1)^i*C(9,i)*(G*x)^(2^(9-i)).

Crossrefs

Column k=9 of A237018.

Sequence in context: A133681 A157553 A202438 * A156273 A051232 A362900

Adjacent sequences: A237021 A237022 A237023 * A237025 A237026 A237027

Keyword

nonn

Author

Alois P. Heinz, Feb 02 2014

Status

approved