A167068 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 5}, {4, 5}}.

11, 6061, 2733511, 1215842661, 540144000000, 239933520731861, 106577890632874111, 47341582784338831461, 21028987835540967334811, 9341012640240002304000000, 4149249488236281570533713211, 1843084039808720108847180812661, 818692341198182161542031245824911

Offset: 1

Author

Paul Raff

Keywords

• nonn

References

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

Links

• P. Raff, Table of n, a(n) for n = 1..200
• P. Raff, Spanning Trees in Grid Graphs, arXiv:0809.2551 [math.CO], 2008.
• P. Raff, Analysis of the Number of Spanning Trees of G x P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 5}, {4, 5}}. Contains sequence, recurrence, generating function, and more.
• P. Raff, Analysis of the Number of Spanning Trees of Grid Graphs.
• 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 Hamiltonian cycles in product graphs
• F. Faase, Results from the counting program
• Index entries for sequences related to trees

Formula

a(n) = 551 a(n-1)

- 51500 a(n-2)

+ 1873400 a(n-3)

- 31993500 a(n-4)

+ 271314053 a(n-5)

- 1157139603 a(n-6)

+ 2669595000 a(n-7)

- 3507446800 a(n-8)

+ 2669595000 a(n-9)

- 1157139603 a(n-10)

+ 271314053 a(n-11)

- 31993500 a(n-12)

+ 1873400 a(n-13)

- 51500 a(n-14)

+ 551 a(n-15)

- a(n-16)

G.f.: -11x (x^14 -3600x^12 +110200x^11 -1112601x^10 +3855898x^9 -4841800x^8 +4841800x^6 -3855898x^5 +1112601x^4 -110200x^3 +3600x^2-1)/(x^16 -551x^15 +51500x^14 -1873400x^13 [phone]x^12 -271314053x^11 [phone]x^10 -2669595000x^9 [phone]x^8 -2669595000x^7 [phone]x^6 -271314053x^5 [phone]x^4 -1873400x^3 +51500x^2 -551x+1).