A167070 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {2, 5}}.

1, 201, 27872, 3656793, 474581525, 61445719296, 7951276371389, 1028790034978377, 133107787044919648, 17221739109190982025, 2228177484370996025801, 288285215706960759705600, 37298804748402271018820409, 4825779209505263485071458889

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}}. 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) = 201 a(n-1)

- 11104 a(n-2)

+ 259893 a(n-3)

- 3001225 a(n-4)

+ 18824856 a(n-5)

- 67848270 a(n-6)

+ 144802410 a(n-7)

- 186068896 a(n-8)

+ 144802410 a(n-9)

- 67848270 a(n-10)

+ 18824856 a(n-11)

- 3001225 a(n-12)

+ 259893 a(n-13)

- 11104 a(n-14)

+ 201 a(n-15)

- a(n-16)

G.f.: -x(x^14 -1425x^12 +26532x^11 -180448x^10 +545916x^9 -661242x^8 +661242x^6 -545916x^5 +180448x^4 -26532x^3 +1425x^2 -1)/ (x^16 -201x^15 +11104x^14 -259893x^13 +3001225x^12 -18824856x^11 [phone]x^10 -144802410x^9 [phone]x^8 -144802410x^7 [phone]x^6 -18824856x^5 +3001225x^4 -259893x^3 +11104x^2 -201x +1).