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 A237019 Number of partitions of the 4-dimensional hypercube resulting from a sequence of n bisections, each of which splits any part perpendicular to any of the axes. 2
 1, 4, 32, 314, 3440, 40320, 494736, 6274900, 81606432, 1082351600, 14583873120, 199075231680, 2747135823040, 38260367077504, 537108342893696, 7592185149935327, 107968131964541240, 1543633250073656032, 22174725274316816504, 319906758044330938320 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 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..4} (-1)^i*C(4,i)*(G*x)^(2^(4-i)). a(n) ~ 1 / (4 * sqrt(Pi) * sqrt(1 - 9*s^2 + 28*s^6 - 30*s^14) * n^(3/2) * r^(n + 1/2)), where r = 0.064125256179778049525781860636169050731447267306296991777... and s = 0.1318780179022368311092675722371337905927964507241063792485... are real roots of the system of equations s + 6*s^4 + s^16 = r + 4*(s^2 + s^8) and 1 + 24*s^3 + 16*s^15 = 8*(s + 4*s^7). - Vaclav Kotesovec, Jun 11 2018 MATHEMATICA Rest[CoefficientList[InverseSeries[Series[x*(1 - 4*x + 6*x^3 - 4*x^7 + x^15), {x, 0, 20}], x], x]] (* Vaclav Kotesovec, Jun 11 2018 *) CROSSREFS Column k=4 of A237018. Sequence in context: A294592 A197715 A369026 * A260155 A047734 A220118 Adjacent sequences: A237016 A237017 A237018 * A237020 A237021 A237022 KEYWORD nonn AUTHOR Alois P. Heinz, Feb 02 2014 STATUS approved

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Last modified August 12 02:57 EDT 2024. Contains 375085 sequences. (Running on oeis4.)