1,1

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

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

P. Raff, Spanning Trees in Grid Graphs. [From Paul Raff (praff(AT)math.rutgers.edu), Mar 06 2009]

P. Raff, Analysis of the Number of Spanning Trees of C_4 x P_n. Contains sequence, recurrence, generating function, and more. [From Paul Raff (praff(AT)math.rutgers.edu), Mar 06 2009]

a(1) = 4,

a(2) = 384,

a(3) = 31500,

a(4) = 2558976,

a(5) = 207746836,

a(6) = 16864848000 and

a(n) = 90a(n-1) - 735a(n-2) + 1548a(n-3) - 735a(n-4) + 90a(n-5) - a(n-6).

G.f.: 4x(x^4+6x^3-30x^2+6x+1)/(x^6-90x^5+735x^4-1548x^3+735x^2-90x+1) [From Paul Raff (praff(AT)math.rutgers.edu), Mar 06 2009]

a(n)=4*A001109(n)*A098301(n). [R. Guy, seqfan list, Mar 28 2009] [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 03 2009]

(Maple) a := n-> (Matrix([[4, 0, -4, -384, -31500, -2558976]]). Matrix(6, (i, j)-> if (i=j-1) then 1 elif j=1 then [90, -735, 1548, -735, 90, -1][i] else 0 fi)^(n-1))[1, 1]; seq (a(n), n=1..12); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 01 2008]

Sequence in context: A154682 A154569 A038015 this_sequence A006237 A116031 A115049

Adjacent sequences: A003750 A003751 A003752 this_sequence A003754 A003755 A003756

nonn

Frans Faase (Frans_LiXia(AT)wxs.nl)

Added recurrence from Faase's web page. - N. J. A. Sloane (njas(AT)research.att.com), Feb 03 2009