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A237024
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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.
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2
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1, 9, 162, 3609, 89910, 2398410, 67006116, 1935501645, 57335681142, 1732321234710, 53177078182860, 1653802745967450, 51997089469768380, 1650038052325122324, 52779255878344803336, 1699938398827907195607, 55085070458854388052090, 1794568569427662345343962
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OFFSET
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0,2
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LINKS
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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.
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FORMULA
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G.f. G satisfies: -x = Sum_{i=0..9} (-1)^i*C(9,i)*(G*x)^(2^(9-i)).
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CROSSREFS
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Column k=9 of A237018.
Sequence in context: A133681 A157553 A202438 * A156273 A051232 A157574
Adjacent sequences: A237021 A237022 A237023 * A237025 A237026 A237027
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Feb 02 2014
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STATUS
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approved
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