A007207 Magnetization for hexagonal lattice. (Formerly M4818)

1, 0, 0, -2, 0, -12, 2, -78, 24, -548, 228, -4050, 2030, -30960, 17670, -242402, 152520, -1932000, 1312844, -15612150, 11297052, -127551884, 97291026, -1051478274, 838994486, -8732657724, 7246304736, -72983051674, 62686156026, -613243234224, 543146222970

Offset

0,4

Comments

The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

References

C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 421.

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

Links

Table of n, a(n) for n=0..30.

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

Shigeo Naya, On the Spontaneous Magnetizations of Honeycomb and Kagomé Ising Lattices, Progress of Theoretical Physics, 11 (1954), 53-62.

G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

Formula

G.f.: (1 - 16 * x^3 / ((1+3*x) * (1-x)^3))^(1/8) [Shigeo Naya]. - Andrey Zabolotskiy, Jun 01 2022

Crossrefs

Cf. A002928, A007206.

Sequence in context: A286648 A321982 A104014 * A349932 A002929 A112261

Adjacent sequences: A007204 A007205 A007206 * A007208 A007209 A007210

Keyword

sign,easy

Author

Simon Plouffe

Extensions

Offset changed, signs of terms changed, and more terms added by Andrey Zabolotskiy, Jun 01 2022

Status

approved