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A136264
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Expansion of (1+x)^2*(x^2-6*x+1)/(x-1)^4.
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3
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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
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0,3
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COMMENTS
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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.
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REFERENCES
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Terrel L. Hill, Statistical Mechanics: Principles and Selected Applications, Dover, New York, 1956, page 331
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LINKS
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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).
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FORMULA
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a(n) = 8n(1-n^2)/3, n>0. [R. J. Mathar, Mar 09 2009]
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MATHEMATICA
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CoefficientList[Series[(1+x)^2(x^2-6x+1)/(x-1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 0, -16, -64, -160}, 40] (* Harvey P. Dale, Mar 15 2020 *)
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PROG
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(PARI) Vec((1+x)^2*(x^2-6*x+1)/(x-1)^4 + O(x^100)) \\ Altug Alkan, Oct 26 2015
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CROSSREFS
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Essentially the same as A102860. Cf. A115046.
Sequence in context: A309573 A205064 A102860 * A266103 A100184 A304845
Adjacent sequences: A136261 A136262 A136263 * A136265 A136266 A136267
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KEYWORD
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sign,easy
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AUTHOR
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Roger L. Bagula, Apr 07 2008
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STATUS
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approved
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