|
| |
|
|
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
|
|
|
|
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
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
