|
| |
|
|
A136264
|
|
Expansion of (1+x)^2*(x^2-6*x+1)/(x-1)^4.
|
|
3
|
|
|
|
1, 0, -16, -64, -160, -320, -560, -896, -1344, -1920, -2640, -3520, -4576, -5824, -7280, -8960, -10880, -13056, -15504, -18240, -21280, -24640, -28336, -32384, -36800, -41600, -46800, -52416, -58464, -64960, -71920, -79360, -87296, -95744, -104720, -114240, -124320, -134976, -146224, -158080
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
Inverse z-transform of the magnetization polynomial for the Ising model.
This polynomial is the eighth power of the spontaneous magnetization for a two-dimensional square lattice.
|
|
|
REFERENCES
|
Terrel L. Hill, Statistical Mechanics: Principles and Selected Applications, Dover, New York, 1956, page 331
|
|
|
LINKS
|
Table of n, a(n) for n=0..39.
M. R. Sepanski, On Divisibility of Convolutions of Central Binomial Coefficients, Electronic Journal of Combinatorics, 21 (1) 2014, #P1.32.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
|
|
|
FORMULA
|
a(n) = 8n(1-n^2)/3, n>0. [R. J. Mathar, Mar 09 2009]
|
|
|
PROG
|
(PARI) Vec((1+x)^2*(x^2-6*x+1)/(x-1)^4 + O(x^100)) \\ Altug Alkan, Oct 26 2015
|
|
|
CROSSREFS
|
Essentially the same as A102860. Cf. A115046.
Sequence in context: A016802 A205064 A102860 * A266103 A100184 A190099
Adjacent sequences: A136261 A136262 A136263 * A136265 A136266 A136267
|
|
|
KEYWORD
|
sign,easy
|
|
|
AUTHOR
|
Roger L. Bagula, Apr 07 2008
|
|
|
STATUS
|
approved
|
| |
|
|
