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A167064 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {4, 5}}. 1
9, 4725, 1990656, 822343725, 338887026225, 139607890329600, 57510072475569441, 23690531503846057725, 9758998421421748936704, 4020088612537397612953125, 1656021591727120808594862489, 682175884126257323680569753600, 281013205982204002882115759532921 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
REFERENCES
F. Faase, On the number of specific spanning subgraphs of the graphs A X P_n, Ars Combin. 49 (1998), 129-154.
LINKS
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.
P. Raff, Spanning Trees in Grid Graphs, arXiv:0809.2551 [math.CO], 2008.
FORMULA
a(n) = 504 a(n-1)
- 40152 a(n-2)
+ 937188 a(n-3)
- 8104008 a(n-4)
+ 27431208 a(n-5)
- 40609478 a(n-6)
+ 27431208 a(n-7)
- 8104008 a(n-8)
+ 937188 a(n-9)
- 40152 a(n-10)
+ 504 a(n-11)
- a(n-12)
G.f.: -9x(x^10 +21x^9 -3264x^8 +37401x^7 -74299x^6 +74299x^4 -37401x^3 +3264x^2 -21x -1)/ (x^12 -504x^11 +40152x^10 -937188x^9 +8104008x^8 -27431208x^7 +40609478x^6 -27431208x^5 +8104008x^4 -937188x^3 +40152x^2 -504x +1).
CROSSREFS
Sequence in context: A193310 A216421 A323337 * A125541 A151581 A145263
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified June 20 08:48 EDT 2024. Contains 373515 sequences. (Running on oeis4.)