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A003780
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Number of spanning trees with degrees 1 and 3 in P_5 X P_n.
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0
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0, 0, 0, 0, 0, 296, 0, 0, 0, 70420, 0, 0, 0, 16391166, 0, 0, 0, 3816021084, 0, 0, 0, 888375830566, 0, 0, 0, 206814474641944, 0, 0, 0, 48146529005876746, 0, 0, 0, 11208539472498838244, 0, 0, 0, 2609354391828066201746, 0, 0, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,6
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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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Table of n, a(n) for n=1..41.
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 28-term linear recurrence on his web page:
a(1) = 0,
a(2) = 0,
a(3) = 0,
a(4) = 0,
a(5) = 0,
a(6) = 296,
a(7) = 0,
a(8) = 0,
a(9) = 0,
a(10) = 70420,
a(11) = 0,
a(12) = 0,
a(13) = 0,
a(14) = 16391166,
a(15) = 0,
a(16) = 0,
a(17) = 0,
a(18) = 3816021084,
a(19) = 0,
a(20) = 0,
a(21) = 0,
a(22) = 888375830566,
a(23) = 0,
a(24) = 0,
a(25) = 0,
a(26) = 206814474641944,
a(27) = 0,
a(28) = 0,
a(29) = 0,
a(30) = 48146529005876746,
a(31) = 0,
a(32) = 0,
a(33) = 0,
a(34) = 11208539472498838244,
a(35) = 0,
a(36) = 0,
a(37) = 0,
a(38) = 2609354391828066201746,
a(39) = 0,
a(40) = 0,
a(41) = 0,
a(42) = 607459192887167645884388,
a(43) = 0,
a(44) = 0,
a(45) = 0,
a(46) = 141416847085185500394182672,
a(47) = 0,
a(48) = 0,
a(49) = 0,
a(50) = 32921922778799648796216249818,
a(51) = 0,
a(52) = 0,
a(53) = 0,
a(54) = 7664242427921761934124201980862,
a(55) = 0,
a(56) = 0,
a(57) = 0,
a(58) = 1784240015038927382237215443432910 and
a(n) = 262a(n-4) - 7125a(n-8) + 78668a(n-12) - 581608a(n-16) + 2138065a(n-20)
- 5215246a(n-24) + 16969316a(n-28) - 43146455a(n-32) + 39514076a(n-36) + 7628882a(n-40)
- 6116529a(n-44) + 23336a(n-48) - 2876a(n-52) + 64a(n-56).
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CROSSREFS
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Sequence in context: A063049 A131274 A074868 * A206339 A107924 A224170
Adjacent sequences: A003777 A003778 A003779 * A003781 A003782 A003783
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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, Feb 03 2009
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STATUS
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approved
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