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Search: id:A116469
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| A116469 |
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Number of spanning trees in an m X n grid read by antidiagonals. |
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+0
2
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| 1, 1, 1, 1, 4, 1, 1, 15, 15, 1, 1, 56, 192, 56, 1, 1, 209, 2415, 2415, 209, 1, 1, 780, 30305, 100352, 30305, 780, 1, 1, 2911, 380160, 4140081, 4140081, 380160, 2911, 1, 1, 10864, 4768673, 170537640, 557568000, 170537640, 4768673, 10864, 1, 1
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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This is the number of ways the points in an m x n grid can be connected to their orthogonal neighbours such that for any pair of points there is precisely one path connecting them
a(n,n) = A007341(n)
a(m,n)= number of perfect mazes made from a grid of m-by-n cells. - Leroy Quet (qq-quet(AT)mindspring.com), Sep 08 2007
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EXAMPLE
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a(2,2) = 4, since we must have exactly 3 of the 4 possible connections: if we have all 4 there are multiple paths between points; if we have fewer some points will be isolated from others.
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CROSSREFS
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Cf. A007341.
Sequence in context: A050154 A058711 A141724 this_sequence A010320 A008304 A118185
Adjacent sequences: A116466 A116467 A116468 this_sequence A116470 A116471 A116472
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KEYWORD
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nonn,tabl
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AUTHOR
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Calculated by Hugo van der Sanden (hv(AT)crypt.org) after a suggestion from Leroy Quet, Mar 20 2006.
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