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A002909
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Low temperature energy function for square lattice.
(Formerly M0035 N0009)
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2
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2, 0, -8, -24, -72, -240, -896, -3640, -15688, -70512, -326968, -1553288, -7523520, -37026704, -184677536, -931655064, -4746324296, -24387839056, -126257024696, -658011767016, -3449826712952, -18183760406080, -96309365029424, -512340286827272
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history;
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internal format)
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OFFSET
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0,1
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REFERENCES
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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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FORMULA
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G.f.: (1+x)/(1-x) + ((1-6*x+x^2)/(1-x^2))*Sum_{k>=0} (2*k)!^2 * (x*(1-x)^2/(1+x)^4)^k/k!^4. - Robert Israel, Nov 27 2017
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MAPLE
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u:=v->((1+v^2)*(1-(2/Pi)*(1-6*v^2+v^4)*EllipticK(4*v*(1-v^2)/(1+v^2)^2)/(1+v^2)^2)/2*v):
S:= series(u((1-v)/(1+v))/((1-v)/(1+v))^2, v, 101):
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MATHEMATICA
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Table[SeriesCoefficient[(1 + v)/(1 - v)^3 ((1 - v)^2 + 2/Pi (1 - 6 v + v^2) EllipticK[(16 v^2)/(1 - v)^4]), {v, 0, k}], {k, 0, 100}] (* Jan Mangaldan, Nov 28 2020 *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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