A167071 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 5}, {3, 5}}.

4, 1376, 361860, 92544256, 23575404820, 6002044445280, 1527898117755412, 388939442019315712, 99007542753465378420, 25203122804459545322080, 6415645979596681028789108, 1633151297922105531036929280, 415731036835959295502046104100, 105827485262836457484100780941664

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, 5}, {3, 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) = 344 a(n-1)

- 25540 a(n-2)

+ 745448 a(n-3)

- 10445708 a(n-4)

+ 76194968 a(n-5)

- 303860988 a(n-6)

+ 687124520 a(n-7)

- 899525622 a(n-8)

+ 687124520 a(n-9)

- 303860988 a(n-10)

+ 76194968 a(n-11)

- 10445708 a(n-12)

+ 745448 a(n-13)

- 25540 a(n-14)

+ 344 a(n-15)

- a(n-16)

G.f.: -4x (x^14 -2331x^12 +56416x^11 -467115x^10 +1546624x^9 -1949983x^8 +1949983x^6 -1546624x^5 +467115x^4 -56416x^3 +2331x^2 -1)/ (x^16 -344x^15 +25540x^14 -745448x^13 [phone]x^12 -76194968x^11 [phone]x^10 -687124520x^9 [phone]x^8 -687124520x^7 [phone]x^6 -76194968x^5 [phone]x^4 -745448x^3 +25540x^2 -344x+1).