A060621 Number of flips between the d-dimensional tilings of the unary zonotope Z(D,d). Here the codimension D-d is equal to 3 and d varies.

12, 36, 100, 264, 672, 1664, 4032, 9600, 22528, 52224

Offset

0,1

References

A. Bjorner, M. Las Vergnas, B. Sturmfels, N. White and G. M. Ziegler, Oriented Matroids, Encyclopedia of Mathematics 46, Second Edition, Cambridge University Press, 1999.

N. Destainville, R. Mosseri and F. Bailly, Fixed-boundary octagonal random tilings: a combinatorial approach, Journal of Statistical Physics, 102 (2001), no. 1-2, 147-190.

Victor Reiner, The generalized Baues problem, in New Perspectives in Algebraic Combinatorics (Berkeley, CA, 1996-1997), 293-336, Math. Sci. Res. Inst. Publ., 38, Cambridge Univ. Press, Cambridge, 1999.

Links

Table of n, a(n) for n=0..9.

M. Latapy, Generalized Integer Partitions, Tilings of Zonotopes and Lattices

Formula

Numbers so far satisfy a(n) = 2^n*(n^2+11n+24)/2. - Ralf Stephan, Apr 08 2004

Empirical g.f.: -4*(7*x^2-9*x+3) / (2*x-1)^3. - Colin Barker, Feb 20 2013

Example

For any Z(d,d), there is a unique tiling therefore the first term of the series is 0. Likewise, there are always two tilings of Z(d+1,d) with a flip between them, therefore the second term of the series is 1.

Crossrefs

Cf. A060595 (number of 3-tilings) for terminology. A diagonal of A060638.

Sequence in context: A033196 A172218 A172212 * A058880 A282097 A055551

Adjacent sequences: A060618 A060619 A060620 * A060622 A060623 A060624

Keyword

nonn

Author

Matthieu Latapy (latapy(AT)liafa.jussieu.fr), Apr 13 2001

Status

approved