A002928 Magnetization for square lattice. (Formerly M1853 N0733)

1, 0, -2, -8, -34, -152, -714, -3472, -17318, -88048, -454378, -2373048, -12515634, -66551016, -356345666, -1919453984, -10392792766, -56527200992, -308691183938, -1691769619240, -9301374102034

Offset

0,3

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

J. M. Yeomans, Statistical mechanics of phase transitions, Oxford Univ. Press, 1992, p. 93.

Links

Table of n, a(n) for n=0..20.

C. Domb, Ising model, Phase Transitions and Critical Phenomena 3 (1974), 257, 380-381, 384-387, 390-391, 412-423. (Annotated scanned copy)

David Park, A summation method for crystal statistics, Physica 22 (1956), 932-940.

Formula

n*a(n) + 6*(-n+1)*a(n-1) + 4*a(n-2) + 6*(n-3)*a(n-3) + (-n+4)*a(n-4) = 0. - R. J. Mathar, Mar 08 2013

a(n) ~ -Gamma(1/8) * (1 + sqrt(2))^(2*n - 1/2) / (Pi * 2^(57/16) * n^(9/8)). - Vaclav Kotesovec, Apr 27 2024

Maple

series((1+x)^(1/4)*(1-6*x+x^2)^(1/8)/(1-x)^(1/2), x, 40).

Mathematica

CoefficientList[Series[(1+x)^(1/4)*(1-6*x+x^2)^(1/8)/(1-x)^(1/2), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 27 2024 *)

Crossrefs

Cf. other structures: A007206, A007207, A002929, A002930, A003193, A003196.

Cf. higher spins: A010102, A010105/A030120, A010103, A010106/A030121, A010104.

Cf. Potts model: A057374, A057378.

Cf. A002927 (susceptibility).

Sequence in context: A150890 A150891 A074606 * A150892 A150893 A235038

Adjacent sequences: A002925 A002926 A002927 * A002929 A002930 A002931

Keyword

sign,easy

Author

N. J. A. Sloane, Simon Plouffe

Status

approved