Animal enumerations on regular tilings in Spherical, Euclidean, and Hyperbolic 2-dimensional spaces

[Jonathan Post]

Dear Tomás Oliveira e Silva,

(1) Would you like me to submit your sequence:
1, 4, 18, 88, 439, 2232, 11522, 60256, 318627, 1700996
named as I suggested (Number of fixed polyominoes in {4,5} tesselation
of the hyperbolic plane, enantiamorphs counted twice), and with the
crossreferences that I suggested, or would you rather submit it to
OEIS under that or similar name?

(2) Is there a hyperbolic tessellation analogue of this nice sequence?:

A010566 Number of 2n-step 2-dimensional closed self-avoiding paths on
square lattice.
0, 8, 24, 112, 560, 2976, 16464, 94016, 549648, 3273040, 19781168,
121020960, 748039552, 4664263744, 29303071680, 185307690240,
1178635456752, 7535046744864, 48392012257184, 312061600211680,
2019822009608592, 13117263660884768, 85447982919036736

OFFSET 	1,2
	
COMMENT 	

a(n)=4n*A002931(n). There are (2n) choices for the starting point and
2 choices for the orientation, in order to produce self-avoiding
closed paths from a polygon of perimeter 2n. -
Philippe.Flajolet(AT)inria.fr, Nov 22, 2003

REFERENCES 	

M. E. Fisher and D. S. Gaunt, Ising model and self-avoiding walks on
hypercubical lattices and high density expansions, Phys. Rev. 133
(1964) A224-A239.

M. E. Fisher and M. F. Sykes, Excluded-volume problem and the Ising
model of ferromagnetism, Phys. Rev. 114 (1959), 45-58.

A. J. Guttmann and I. G. Enting, The size and number of rings on the
square lattice, J. Phys. A 21 (1988), L165-L172.

B. J. Hiley and M. F. Sykes, Probability of initial ring closure in
the restricted random-walk model of a macromolecule, J. Chem. Phys.,
34 (1961), 1531-1537.

B. Hayes, How to avoid yourself, American Scientist, Vol. 86, Number
4, Jul-August 1998. p. 314-319.

B. D. Hughes, Random Walks and Random Environments, Oxford 1995, vol. 1, p. 461.

G. S. Rushbrooke and J. Eve, "On Noncrossing Lattice Polygons",
Journal of Chemical Physics, 31 (1959), 1333-1334.

LINKS 	

I. Jensen, More terms

KEYWORD nonn,nice

AUTHOR 	njas




Dear Seqfans and Assoc. Editors,
Around 12:00 - 14:00 New York time today the sytems people here
made a number of changes to the local computers.   I was in
the middle of a big update of the OEIS.  Mail stopped working.
I hope nothing was lost and nothing was broken.  I redid the update
and there is now a new version of the OEIS.
(I am still about a week behind with Comments,
and a few days behind in processing new sequences)

Neil