login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A237026 Number of partitions of the n-dimensional hypercube resulting from a sequence of n bisections, each of which splits any part perpendicular to any of the axes. 3
1, 1, 8, 132, 3440, 124250, 5770692, 328480502, 22171138432, 1732321234710, 153860041920200, 15314241603864346, 1688777066667724992, 204402336519440816068, 26942653699545370953376, 3842033763551789263983510, 589364606143191408040312960 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..130

FORMULA

a(n) = [x^n] G_n, where G_n satisfies: (-1)^n*x = Sum_{i=0..n} (-1)^i*C(n,i)*(G_n*x)^(2^(n-i)).

a(n) ~ 2^(2*n) * n^(n - 3/2) / (sqrt(Pi) * exp(1/8)). - Vaclav Kotesovec, Jun 11 2018

MATHEMATICA

b[n_, k_, t_] := b[n, k, t] = If[t==0, 1, If[t==1, A[n-1, k], Sum[A[j, k]* b[n-j-1, k, t-1], {j, 0, n-2}]]];

a[n_] := If[n==0, 1, -Sum[Binomial[n, j]*(-1)^j*b[n+1, n, 2^j], {j, 1, n}]];

a /@ Range[0, 16] (* Jean-Fran├žois Alcover, Oct 19 2019, after Alois P. Heinz in A237018 *)

CROSSREFS

Main diagonal of A237018.

Cf. A300474.

Sequence in context: A241076 A349683 A222429 * A079912 A281948 A128287

Adjacent sequences:  A237023 A237024 A237025 * A237027 A237028 A237029

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 02 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 17 17:47 EST 2022. Contains 350402 sequences. (Running on oeis4.)