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A002890
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Low temperature series for spin-1/2 Ising partition function on 2D square lattice.
(Formerly M1463 N0578)
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8
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1, 0, 1, 2, 5, 14, 44, 152, 566, 2234, 9228, 39520, 174271, 787246, 3628992, 17019374, 81011889, 390633382, 1905134695, 9385453576, 46653815395, 233788460256, 1180111379105, 5996452414310, 30653752894948
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OFFSET
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0,4
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 391-406.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MATHEMATICA
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(* For 25 terms, a PC computation lasts less than half an hour *) m = 48 (* max y exponent *); coes = CoefficientList[ Series[ Log[(1 + y^2)^2 - 2*y*(1 - y^2)*(Cos[2*Pi*u] + Cos[2*Pi*v])], {y, 0, m}], y] // Rest; nint[f_, {n_}] := If[n == 2 || OddQ[n], 0, Print[n]; Integrate[ Integrate[f, {u, 0, 1}], {v, 0, 1}]]; fy = MapIndexed[nint, coes].Table[y^k, {k, 1, m}]; CoefficientList[ Series[ Exp[fy/2], {y, 0, m}] , y^2] (* Jean-François Alcover, Mar 19 2013 *)
CoefficientList[(1+u) Exp[-x HypergeometricPFQ[{1, 1, 3/2, 3/2}, {2, 2, 2}, 16x] /. {x -> (u (1 - u)^2)/(1 + u)^4}] + O[u]^50, u] (* Andrey Zabolotskiy, Feb 12 2022, using the g. f. from Gandhimohan M. Viswanathan, 2014-2015 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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"Free energy" changed back to "partition function" (basically the exponential of the free energy) in the name by Andrey Zabolotskiy, Feb 11 2022
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STATUS
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approved
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