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A139400
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Number of spanning trees in the graph P_6 x P_n.
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3
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1, 780, 380160, 170537640, 74795194705, 32565539635200, 14143261515284447, 6136973985625588560, 2662079368040434932480, 1154617875754582889149500, 500769437567956298239402223, 217185579535490113365186969600
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also number of domino tilings of the 11 X (2n-1) rectangle with upper left corner removed. - Alois P. Heinz, Apr 14 2011
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LINKS
| P. Raff, Table of n, a(n) for n=1..208
Paul Raff, Spanning Trees in Grid Graphs, arXiv:0809.2551 [math.CO]
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FORMULA
| a(n) = 780 a(n - 1) - 194881 a(n - 2) + 22377420 a(n - 3) - 1419219792 a(n - 4) + 55284715980 a(n - 5) - 1410775106597 a(n - 6) + 24574215822780 a(n - 7) - 300429297446885 a(n - 8) + 2629946465331120 a(n - 9) - 16741727755133760 a(n - 10)
+ 78475174345180080 a(n - 11) - 273689714665707178 a(n - 12) + 716370537293731320 a(n - 13) - 1417056251105102122 a(n - 14) + 2129255507292156360 a(n - 15) - 2437932520099475424 a(n - 16) + 2129255507292156360 a(n - 17)
- 1417056251105102122 a(n - 18) + 716370537293731320 a(n - 19) - 273689714665707178 a(n - 20) + 78475174345180080 a(n - 21) - 16741727755133760 a(n - 22) + 2629946465331120 a(n - 23) - 300429297446885 a(n - 24) + 24574215822780 a(n - 25) - 1410775106597 a(n - 26) + 55284715980 a(n - 27) - 1419219792 a(n - 28) + 22377420 a(n - 29) - 194881 a(n - 30) + 780 a(n - 31) - a(n - 32)
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EXAMPLE
| a(2) = 780, as can be verified from the seventh entry of A001353, which corresponds to the number of spanning trees of the same graph.
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CROSSREFS
| Sequence in context: A200559 A147547 A135198 * A115467 A020231 A038477
Adjacent sequences: A139397 A139398 A139399 * A139401 A139402 A139403
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Raff (praff(AT)math.rutgers.edu), Jun 09 2008; corrected recurrence Feb 03 2009
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