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A003685 Number of Hamiltonian paths in P_3 X P_n. 1
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; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

LINKS

Table of n, a(n) for n=1..28.

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

FORMULA

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, 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, Dec 05 2007

CROSSREFS

Sequence in context: A179756 A238507 A101363 * A066011 A007016 A129550

Adjacent sequences:  A003682 A003683 A003684 * A003686 A003687 A003688

KEYWORD

nonn

AUTHOR

Frans J. Faase

STATUS

approved

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Last modified May 23 06:42 EDT 2017. Contains 286909 sequences.