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Search: id:A007341
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| A007341 |
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Number of spanning trees in n X n grid.
(Formerly M3721)
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+0
4
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| 1, 4, 192, 100352, 557568000, 32565539635200, 19872369301840986112, 126231322912498539682594816, 8326627661691818545121844900397056, 5694319004079097795957215725765328371712000, 40325021721404118513276859513497679249183623593590784, 2954540993952788006228764987084443226815814190099484786032640000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Kreweras calls this the complexity of the n X n grid.
a(n) = 2^(n^2-1) / n^2 * product_{n1=0..n-1, n2=0..n-1, n1 and n2 not both 0} (2 - cos(PI*n1/n) - cos(PI*n2/n) ). - Sharon Sela (sharonsela(AT)hotmail.com), Jun 04 2002
a(n)= number of perfect mazes made from a grid of n-by-n cells. - Leroy Quet Sep 08 2007
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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).
G. Kreweras, Complexite et circuits Euleriens dans la sommes tensorielles de graphes, J. Combin. Theory, B 24 (1978), 202-212.
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
W.-J. Tzeng, F. Y. Wu, Spanning Trees on Hypercubic Lattices and Non-orientable Surfaces.
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CROSSREFS
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Cf. A116469.
Sequence in context: A163839 A012015 A012102 this_sequence A159783 A028370 A042127
Adjacent sequences: A007338 A007339 A007340 this_sequence A007342 A007343 A007344
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms and better description from Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 07 2002
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