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A167058 Number of spanning trees in (S_5 + e) X P_n. 1
3, 945, 221184, 50055705, 11275732875, 2538325278720, 571357349020731, 128606300878893705, 28947814696524275712, 6515821689652895090625, 1466636804229895456081107, 330123137841949620861665280, 74306935243221668928140352051 (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 (S_5 + e) x P_n. 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

Index entries for linear recurrences with constant coefficients, signature (270, -10529, 95310, -177156, 95310, -10529, 270, -1).

FORMULA

a(n) = 270 a(n-1)

- 10529 a(n-2)

+ 95310 a(n-3)

- 177156 a(n-4)

+ 95310 a(n-5)

- 10529 a(n-6)

+ 270 a(n-7)

- a(n-8)

G.f.: -3x(x^6 +45x^5 -793x^4 +793x^2 -45x -1)/ (x^8 -270x^7 +10529x^6 -95310x^5 +177156x^4 -95310x^3 +10529x^2 -270x +1)

MATHEMATICA

CoefficientList[Series[-3x (x^6+45x^5-793x^4+793x^2-45x-1)/(x^8-270x^7+ 10529x^6-95310x^5+177156x^4-95310x^3+10529x^2-270x+1), {x, 0, 30}], x] (* or *) LinearRecurrence[{270, -10529, 95310, -177156, 95310, -10529, 270, -1}, {0, 3, 945, 221184, 50055705, 11275732875, 2538325278720, 571357349020731}, 30] (* Harvey P. Dale, Nov 22 2021 *)

CROSSREFS

Sequence in context: A094592 A210768 A332193 * A167067 A324443 A151585

Adjacent sequences:  A167055 A167056 A167057 * A167059 A167060 A167061

KEYWORD

nonn

AUTHOR

Paul Raff

STATUS

approved

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Last modified January 21 17:55 EST 2022. Contains 350479 sequences. (Running on oeis4.)