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).

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

Cf. A238835, A238836.

Sequence in context: A246820 A094237 A016654 * A270827 A293072 A120447

Adjacent sequences: A090670 A090671 A090672 * A090674 A090675 A090676

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