

A003745


Number of spanning trees in (K_5  e) X P_n.


1




OFFSET

1,1


REFERENCES

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129154.


LINKS

P. Raff, Table of n, a(n) for n = 1..200
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), 129154.
F. Faase, Counting Hamiltonian cycles in product graphs
F. Faase, Results from the counting program
P. Raff, Spanning Trees in Grid Graphs.
P. Raff, Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {3, 4}}. Contains sequence, recurrence, generating function, and more.
P. Raff, Analysis of the Number of Spanning Trees of Grid Graphs.


FORMULA

a(n) = 1645*a(n1)  160129*a(n2) + 3747310*a(n3)  7579606*a(n4) + 3747310*a(n5)  160129*a(n6) + 1645*a(n7)  a(n8).  Modified by Paul Raff, Oct 29 2009
G.f.: 75x(x^6 + 70x^5  6838x^4 + 6838x^2  70x  1)/(x^8  1645x^7 + 160129x^6  3747310x^5 + 7579606x^4  3747310x^3 + 160129x^2  1645x + 1).  Paul Raff, Oct 29 2009
a(n) = 75*A001906(n)*(A004187(n))^3 [R. K. Guy, via seqfan list, Mar 28 2009].  R. J. Mathar, Jun 03 2009


MATHEMATICA

75 LinearRecurrence[{1645, 160129, 3747310, 7579606, 3747310, 160129, 1645, 1}, {1, 1715, 2654208, 4095298235, 6318168987625, 9747545118474240, 15038315878675313497, 23200810075172537929835}, 20] (* JeanFrançois Alcover, Oct 07 2018 *)


CROSSREFS

Sequence in context: A263064 A085404 A110100 * A301468 A068942 A116234
Adjacent sequences: A003742 A003743 A003744 * A003746 A003747 A003748


KEYWORD

nonn


AUTHOR

Frans J. Faase


EXTENSIONS

Added recurrence from Faase's web page.  N. J. A. Sloane, Feb 03 2009


STATUS

approved



