login
A090673
Large-q series expansion for exponential of bulk free energy of the square-lattice zero-temperature Potts antiferromagnet, divided by (q-1)^2/q, in terms of the variable z = 1/(q - 1).
3
1, 0, 0, 1, 0, 0, 0, 1, 3, 4, 3, 3, 11, 24, 8, -91, -261, -290, 254, 1671, 3127, 786, -13939, -49052, -80276, 21450, 515846, 1411017, 1160761, -4793764, -20340586, -29699360, 33165914, 256169433, 495347942, -127736296, -3068121066, -7092358808, -1024264966, 35697720501, 91243390558, 25789733672, -420665229170, -1089052872105, -238516756366, 5101697398582, 12146149238921
OFFSET
0,9
COMMENTS
Related to chromatic polynomial of the infinite square grid.
REFERENCES
N. Biggs, Algebraic Graph Theory, Cambridge, 2nd. Ed., 1993, p. 96.
LINKS
Andrey Zabolotskiy, Table of n, a(n) for n = 0..79 (from Jacobsen 2010)
Jesper Lykke Jacobsen, Bulk, surface and corner free-energy series for the chromatic polynomial on the square and triangular lattices, J. Phys. A: Math. Theor., 43 (2010), 315002; arXiv:1005.3609 [cond-mat.stat-mech], 2010.
D. Kim and I. G. Enting, The limit of chromatic polynomials, J. Combin. Theory B26 (1979), 327-336.
J. Salas and A. D. Sokal, Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial, J. Stat. Phys. 135 (2009) 279-373, arXiv:0711.1738 [cond-mat.stat-mech], 2007-2009.
CROSSREFS
Sequence in context: A246820 A094237 A016654 * A270827 A293072 A120447
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Dec 18 2003
EXTENSIONS
More terms from Salas-Sokal, 2009. - N. J. A. Sloane, Mar 14 2014
Name corrected by Andrey Zabolotskiy, Feb 11 2022
STATUS
approved