A167058 Number of spanning trees in (S_5 + e) X P_n.

3, 945, 221184, 50055705, 11275732875, 2538325278720, 571357349020731, 128606300878893705, 28947814696524275712, 6515821689652895090625, 1466636804229895456081107, 330123137841949620861665280, 74306935243221668928140352051

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
• 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, arXiv:0809.2551 [math.CO], 2008.
• 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).

Programs

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 *)

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)