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A136264
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Expansion of g.f. (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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This g.f. is the eighth power of the spontaneous magnetization series for the two-dimensional square lattice in the parameter x = exp(-4J/kT), cf. A002928.
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REFERENCES
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Terrel L. Hill, Statistical Mechanics: Principles and Selected Applications, Dover, New York, 1956, page 331. See eq. 44.12 for the g.f. with x replaced by x^2.
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LINKS
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FORMULA
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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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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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