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A237021
Number of partitions of the 6-dimensional hypercube resulting from a sequence of n bisections, each of which splits any part perpendicular to any of the axes.
2
1, 6, 72, 1065, 17604, 311472, 5770692, 110530514, 2171011800, 43490709702, 885138113016, 18250712631216, 380432844142092, 8003697071972760, 169728054535951520, 3624215619984643650, 77857888349211858000, 1681568232191988128040, 36491768084579204728800
OFFSET
0,2
LINKS
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..6} (-1)^i*C(6,i)*(G*x)^(2^(6-i)).
CROSSREFS
Column k=6 of A237018.
Sequence in context: A370098 A303342 A332705 * A156128 A052678 A052719
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 02 2014
STATUS
approved