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A005389
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Number of Hamiltonian circuits on 2n times 4 rectangle.
(Formerly M4228)
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1
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1, 6, 37, 236, 1517, 9770, 62953, 405688, 2614457, 16849006, 108584525, 699780452, 4509783909, 29063617746, 187302518353, 1207084188912, 7779138543857, 50133202843990, 323086934794997, 2082156365731164, 13418602439355485, 86477122654688250, 557307869909156153
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OFFSET
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1,2
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REFERENCES
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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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Vincenzo Librandi, Table of n, a(n) for n = 1..200
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
T. G. Schmalz, G. E. Hite and D. J. Klein, Compact self-avoiding circuits on two-dimensional lattices, J. Phys. A 17 (1984), 445-453.
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FORMULA
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G.f.: x*(1-2*x-x^2)/(1-8*x+10*x^2+x^4). - Ralf Stephan, Apr 23 2004
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MAPLE
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A005389:=-(-1+2*z+z**2)/(1-8*z+10*z**2+z**4); [Conjectured by Simon Plouffe in his 1992 dissertation.]
a:= n -> (Matrix([[0, 1, 2, -11]]). Matrix(4, (i, j)-> if (i=j-1) then 1 elif j=1 then [8, -10, 0, -1][i] else 0 fi)^(n))[1, 1]: seq (a(n), n=1..25); # Alois P. Heinz, Aug 05 2008
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MATHEMATICA
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a[1]=1; a[2]=6; a[3]=37; a[4]=236; a[n_] := a[n] = 8*a[n-1]-10*a[n-2]-a[n-4]; Array[a, 23] (* Jean-François Alcover, Mar 13 2014 *)
CoefficientList[Series[(1 - 2 x - x^2)/(1 - 8 x + 10 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Mar 15 2014 *)
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CROSSREFS
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Bisection of A006864.
Sequence in context: A218186 A154623 A196834 * A080954 A271905 A351152
Adjacent sequences: A005386 A005387 A005388 * A005390 A005391 A005392
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Simon Plouffe
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STATUS
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approved
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