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Search: id:A003682
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| A003682 |
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Number of Hamiltonian paths in K_2 X P_n. |
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+0
3
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| 1, 4, 8, 14, 22, 32, 44, 58, 74, 92, 112, 134, 158, 184, 212, 242, 274, 308, 344, 382, 422, 464, 508, 554, 602, 652, 704, 758, 814, 872, 932, 994, 1058, 1124, 1192, 1262, 1334, 1408, 1484, 1562, 1642, 1724, 1808, 1894, 1982, 2072, 2164
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Equals row sums of triangle A144336 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 18 2008]
Except for the first term, a(n)=2*n+a(n-1), (with a(1)=4) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 23 2009]
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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
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FORMULA
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For n>1, a(n) = n^2 - n + 2.
Equals binomial transform of [1, 3, 1, 1, -1, 1, -1, 1,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 23 2008
G.f.: x(1+x-x^2+x^3)/(1-x)^3. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 16 2008]
Except for the first term, a(n)=2*n+a(n-1), (with a(1)=4) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 23 2009]
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EXAMPLE
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Fon=2, a(2)=2*2+4=8, n=3, a(3)=2*3+8=14; n=4, a(4)=2*4+14=22 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 23 2009]
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MAPLE
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a:=n->sum(binomial(2, 2*j)+n, j=0..n): seq(a(n), n=0..46); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2007
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CROSSREFS
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Equals A002061(n) + 1, n>1.
Cf. A144336 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 18 2008]
Adjacent sequences: A003679 A003680 A003681 this_sequence A003683 A003684 A003685
Sequence in context: A053459 A024398 A054347 this_sequence A011897 A110895 A049628
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KEYWORD
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nonn,new
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AUTHOR
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Frans Faase (Frans_LiXia(AT)wxs.nl)
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