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A162483
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a(n) is the number of perfect matchings of an edge-labeled 2 x (2n+1) Mobius grid graph.
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0
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3, 6, 13, 31, 78, 201, 523, 1366, 3573, 9351, 24478, 64081, 167763, 439206, 1149853, 3010351, 7881198, 20633241, 54018523, 141422326, 370248453, 969323031, 2537720638, 6643838881, 17393796003
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| This is a specialization for m=2 of a general formula for the number of perfect matchings of an edge-labeled m x (2n+1) Mobius grid graph.
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REFERENCES
| G. Tesler, Matchings in Graphs on Non-Orientable Surfaces, Journal of Combinatorial Theory, Series B, 78(2000), 198-231.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (4,-4,1).
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FORMULA
| a(n) = Re((1-i)(\frac{L_(2n+1)-F_(2n+1)}{2}+F_{(2n+1)+1}+2i))
Conjecture: a(n)=4*a(n-1)-4*a(n-2)+a(n-3). G.f.: -(3-6*x+x^2)/((x-1)*(x^2-3*x+1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 08 2009]
a(n+1)-a(n) = A005248(n+1). [R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 18 2010]
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EXAMPLE
| a(0) = 3 because this is the number of perfect matchings of a 2 x 1 Mobius grid graph (one for each of the three multiple edges).
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MATHEMATICA
| Re[(1 - I) (2 I + Fibonacci[2 + 2 n] + 1/2 (-Fibonacci[1 + 2 n] + LucasL[1 + 2 n]))
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CROSSREFS
| Cf. A020878
Sequence in context: A130582 A126296 A018014 * A179928 A026538 A201951
Adjacent sequences: A162480 A162481 A162482 * A162484 A162485 A162486
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KEYWORD
| nonn,easy
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AUTHOR
| Sarah-Marie Belcastro (smbelcas(AT)toroidalsnark.net), Jul 04 2009
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