A167059 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}}.

8, 4032, 1612800, 631427328, 246562692200, 96244833484800, 37566939748080392, 14663279200231130112, 5723424260979717196800, 2233987356983360324068800, 871977888467614764819315368, 340353508793721676084268236800, 132847991246505889127220947758952

Offset: 1

Author

Paul Raff, Jun 01 2010

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
• 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
• 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}, {1, 5}, {2, 3}, {2, 4}}. Contains sequence, recurrence, generating function, and more.
• P. Raff, Analysis of the Number of Spanning Trees of Grid Graphs.
• Index entries for sequences related to trees

Formula

a(n) = 504 a(n-1)

- 48706 a(n-2)

+ 1765008 a(n-3)

- 29021617 a(n-4)

+ 239655024 a(n-5)

- 1039298722 a(n-6)

+ 2447629128 a(n-7)

- 3242171236 a(n-8)

+ 2447629128 a(n-9)

- 1039298722 a(n-10)

+ 239655024 a(n-11)

- 29021617 a(n-12)

+ 1765008 a(n-13)

- 48706 a(n-14)

+ 504 a(n-15)

- a(n-16)

G.f.: -8x (x^14 -3710x^12 +104832x^11 -997954x^10 +3633840x^9 -4759203x^8 +4759203x^6 -3633840x^5 +997954x^4 -104832x^3 +3710x^2-1)/ (x^16 -504x^15 +48706x^14 -1765008x^13 [phone]x^12 -239655024x^11 [phone]x^10 -2447629128x^9 [phone]x^8 -2447629128x^7 [phone]x^6 -239655024x^5 [phone]x^4 -1765008x^3 +48706x^2 -504x+1).