|
| |
|
|
A003691
|
|
Number of spanning trees with degrees 1 and 3 in K_3 X P_2n.
|
|
1
| |
|
|
3, 36, 324, 2880, 25632, 228096, 2029824, 18063360, 160745472, 1430470656, 12729729024, 113281597440, 1008090611712, 8970977673216, 79832546279424, 710428191621120
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
REFERENCES
| F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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 Hamilton cycles in product graphs
F. Faase, Results from the counting program
F. Faase, Counting Hamilton cycles in product graphs
Index entries for sequences related to trees
Index to sequences with linear recurrences with constant coefficients, signature (8,8).
|
|
|
FORMULA
| a(n) = 8*a(n-1) + 8*a(n-2), n>3.
G.f.: 3*x*(1+2*x)^2/(1-8*x-8*x^2). For n>1, a(n) = 3*sqrt(3)*sqrt(2^(2*n-7))*((2+sqrt(6))^n-(2-sqrt(6))^n) - Bruno Berselli, Aug 02 2011
|
|
|
PROG
| (MAGMA) i:=[3, 36, 324]; [n le 3 select i[n] else 8*(Self(n-1)+Self(n-2)): n in [1..16]]; // Bruno Berselli, Aug 02 2011
|
|
|
CROSSREFS
| Cf. A057091.
Sequence in context: A056299 A073980 A034860 * A038146 A067444 A092648
Adjacent sequences: A003688 A003689 A003690 * A003692 A003693 A003694
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Frans Faase (Frans_LiXia(AT)wxs.nl)
|
| |
|
|
