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Search: id:A003762
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| A003762 |
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Number of spanning trees with degrees 1 and 3 in D_4 X P_n. |
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+0
1
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| 1, 4, 16, 92, 432, 1884, 8582, 39736, 181936, 829672, 3793850, 17366388, 79441576, 363298928, 1661695126, 7601017276, 34767611570, 159026305464, 727389859704, 3327116203688, 15218354613018, 69609219627912
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
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LINKS
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F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
F. Faase, Counting Hamilton cycles in product graphs
F. Faase, Results from the counting program
F. Faase, Counting Hamilton cycles in product graphs
Index entries for sequences related to trees
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FORMULA
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Faase gives a 12-term linear recurrence on his web page:
a(1) = 1,
a(2) = 4,
a(3) = 16,
a(4) = 92,
a(5) = 432,
a(6) = 1884,
a(7) = 8582,
a(8) = 39736,
a(9) = 181936,
a(10) = 829672,
a(11) = 3793850,
a(12) = 17366388,
a(13) = 79441576,
a(14) = 363298928,
a(15) = 1661695126 and
a(n) = 4a(n-1) - 5a(n-2) + 30a(n-3) + 13a(n-4) + 36a(n-5) + 48a(n-6) - 76a(n-7) - 14a(n-8) - 36a(n-9) + 4a(n-10) + 8a(n-11) - 4a(n-12).
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CROSSREFS
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Sequence in context: A124962 A009568 A139155 this_sequence A143501 A111291 A050913
Adjacent sequences: A003759 A003760 A003761 this_sequence A003763 A003764 A003765
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KEYWORD
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nonn
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AUTHOR
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Frans Faase (Frans_LiXia(AT)wxs.nl)
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EXTENSIONS
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Added recurrence from Faase's web page. - N. J. A. Sloane (njas(AT)research.att.com), Feb 03 2009
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