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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
| G.f.: (1-2x-x^2)/(1-8x+10x^2+x^4). - Ralf Stephan, Apr 23 2004
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MAPLE
| A005389:=-(-1+2*z+z**2)/(1-8*z+10*z**2+z**4); [Conjectured by S. Plouffe in his 1992 dissertation.]
(Maple) 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..18); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 05 2008]
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CROSSREFS
| Bisection of A006864.
Sequence in context: A081188 A154623 A196834 * A080954 A073013 A192238
Adjacent sequences: A005386 A005387 A005388 * A005390 A005391 A005392
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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