A141770 Number of recursively combed cube orientations.

1, 2, 12, 680, 3209712, 94504354122272, 100812007252263643279948656576, 135585824090362207213177704090990942335416773530694383100032, 282570867266578830058415920864613996799733445645033376671698734585656490069707720544980164859900048942541095947330649856

Offset

0,2

Comments

An orientation of the edges of the d-dimensional hypercube is recursively combed if there is at least one dimension along which all the edges go into the same direction and the two (d-1)-dimensional cube orientations resulting from the removal of all edges along that dimension are again recursively combed.

References

GWOP 2008, 6th Gremo Workshop on Open Problems

Links

Table of n, a(n) for n=0..8.

Formula

f(n) = sum((-1)^(j+1)*2^j*binomial(n,j)*f(n-j)^(2^j), j=1..n), f(0) = 1

Maple

f[0] := 1; for k from 1 to 8 do f[k] := sum((-1)^(j+1)*2^j*binomial(k, j)*f[k-j]^(2^j), j=1..k); od;

Crossrefs

Sequence in context: A216335 A173104 * A363098 A230265 A060055 A363234

Adjacent sequences: A141767 A141768 A141769 * A141771 A141772 A141773

Keyword

nonn

Author

Philipp Zumstein (zuphilip(AT)inf.ethz.ch), Sep 16 2008

Status

approved