A167072 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 5}, {3, 5}, {4, 5}}.

12, 6720, 3110400, 1423806720, 651286330860, 297900675072000, 136260356109480876, 62325740425973498880, 28507909150300692211200, 13039570449847302883368000, 5964323676112090939594326348, 2728092696767010687412666368000, 1247834652562251646622689145644236

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}, {2, 5}, {3, 5}, {4, 5}}. 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) = 525 a(n-1)

- 32415 a(n-2)

+ 696920 a(n-3)

- 5936265 a(n-4)

+ 19827675 a(n-5)

- 29313582 a(n-6)

+ 19827675 a(n-7)

- 5936265 a(n-8)

+ 696920 a(n-9)

- 32415 a(n-10)

+ 525 a(n-11)

- a(n-12).

G.f.: -12x (x^10 +35x^9 -2385x^8 +26040x^7 -54030x^6 +54030x^4 -26040x^3 +2385x^2 -35x-1) / (x^12 -525x^11 +32415x^10 -696920x^9 +5936265x^8 -19827675x^7 [phone]x^6 -19827675x^5 +5936265x^4 -696920x^3 +32415x^2 -525x+1).