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Search: id:A003685
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| A003685 |
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Number of Hamilton paths in P_3 X P_n. |
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+0
1
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| 1, 8, 20, 62, 132, 336, 688, 1578, 3190, 6902, 13878, 29038, 58238, 119518, 239390, 485822, 972414, 1960830, 3923326, 7882494, 15768574, 31616510, 63240702, 126655486, 253327358, 507033598, 1014102014, 2029023230
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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F. Faase, Counting Hamilton cycles in product graphs
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FORMULA
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a(n) = 3a(n-1) + 2a(n-2) - 12a(n-3) + 4a(n-4) + 12a(n-5) - 8a(n-6), n>8.
a(2m) = 121*2^(2m-4) - 4m*2^m - 25*2^(m-2) - 2, m > 1; a(2m+1) = 121*2^(2m-3) - 31m*2^(m-2) - 23*2^(m-1) - 2, m > 0. Simpler recurrence relation: a(n) = 8a(n-2) - 20a(n-4) + 16a(n-6) + 6, n > 8. - David Bevan (dbevan(AT)emtex.com), Jul 21 2006
O.g.f.: (2*x^7-8*x^6+12*x^5-2*x^4-2*x^3-6*x^2+5*x+1)*x/((2*x-1)*(-1+2*x^2)^2*(-1+x)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 05 2007
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CROSSREFS
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Sequence in context: A107816 A036835 A101363 this_sequence A066011 A007016 A129550
Adjacent sequences: A003682 A003683 A003684 this_sequence A003686 A003687 A003688
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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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