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A167062 Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {3, 4}} 1
16, 12096, 7526400, 4600399104, 2805387952400, 1710196656537600, 1042505162050645904, 635487948490723808256, 387378914569568374118400, 236137288417488262321070400, 143943863916057463999036728976, 87744870926093811441456945561600, 53487256495669025156132129844140944 (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

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.

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}, {3, 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) = 735 a(n-1)

- 80115 a(n-2)

+ 2269596 a(n-3)

- 23630145 a(n-4)

+ 89290005 a(n-5)

- 139636406 a(n-6)

+ 89290005 a(n-7)

- 23630145 a(n-8)

+ 2269596 a(n-9)

- 80115 a(n-10)

+ 735 a(n-11)

- a(n-12)

G.f.: -16x(x^10 +21x^9 -5145x^8 +78288x^7 -175246x^6 +175246x^4 -78288x^3 +5145x^2 -21x -1)/ (x^12 -735x^11 +80115x^10 -2269596x^9 +23630145x^8 -89290005x^7 +139636406x^6 -89290005x^5 +23630145x^4 -2269596x^3 +80115x^2 -735x +1)

CROSSREFS

Sequence in context: A191945 A290770 A223102 * A233140 A249968 A017188

Adjacent sequences:  A167059 A167060 A167061 * A167063 A167064 A167065

KEYWORD

nonn,easy

AUTHOR

Paul Raff

STATUS

approved

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Last modified July 2 10:39 EDT 2022. Contains 355004 sequences. (Running on oeis4.)