A237022 Number of partitions of the 7-dimensional hypercube resulting from a sequence of n bisections, each of which splits any part perpendicular to any of the axes.

1, 7, 98, 1694, 32732, 677082, 14667072, 328480502, 7544198956, 176717178176, 4205620508824, 101400381318782, 2471618555755972, 60805104853528336, 1507824418684909472, 37649597045144908852, 945799864583981705872, 23887043176751274744168

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..7} (-1)^i*C(7,i)*(G*x)^(2^(7-i)).

Crossrefs

Column k=7 of A237018.

Sequence in context: A133679 A219406 A267664 * A156266 A234873 A051188

Adjacent sequences: A237019 A237020 A237021 * A237023 A237024 A237025

Keyword

nonn

Author

Alois P. Heinz, Feb 02 2014

Status

approved