

A136264


Expansion of (1+x)^2*(x^26*x+1)/(x1)^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
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OFFSET

0,3


COMMENTS

Inverse ztransform of the magnetization polynomial for the Ising model.
This polynomial is the eighth power of the spontaneous magnetization for a twodimensional 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(1n^2)/3, n>0. [R. J. Mathar, Mar 09 2009]


MATHEMATICA

CoefficientList[Series[(1+x)^2(x^26x+1)/(x1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, 6, 4, 1}, {1, 0, 16, 64, 160}, 40] (* Harvey P. Dale, Mar 15 2020 *)


PROG

(PARI) Vec((1+x)^2*(x^26*x+1)/(x1)^4 + O(x^100)) \\ Altug Alkan, Oct 26 2015


CROSSREFS

Essentially the same as A102860. Cf. A115046.
Sequence in context: A309573 A205064 A102860 * A266103 A100184 A304845
Adjacent sequences: A136261 A136262 A136263 * A136265 A136266 A136267


KEYWORD

sign,easy


AUTHOR

Roger L. Bagula, Apr 07 2008


STATUS

approved



