|
| |
|
|
A158450
|
|
Number of spanning forests in 3 X n grid.
|
|
0
| |
|
|
4, 112, 3102, 85818, 2373870, 65664106, 1816344222, 50242141946, 1389754592846, 38442187035914, 1063354458854270, 29413589398458778, 813613216256931886, 22505463603889302698, 622526628016224886878, 17219792020736937982522
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
FORMULA
| G.f.: (4*x^4-22*x^3+20*x^2-4*x) / (33*x-154*x^2+176*x^3-32*x^4-1).
|
|
|
EXAMPLE
| For n = 1 the a(1) = 4 forests are 1.2.3, 1-2.3, 1.2-3, 1-2-3.
|
|
|
MAPLE
| a:= n-> (Matrix([[112, 4, 1/8, 0]]). Matrix(4, (i, j)-> if i=j-1 then 1 elif j=1 then [33, -154, 176, -32][i] else 0 fi)^n)[1, 3]: seq (a(n), n=1..20);
|
|
|
CROSSREFS
| Sequence in context: A202518 A181485 A135917 * A063406 A013151 A006718
Adjacent sequences: A158447 A158448 A158449 * A158451 A158452 A158453
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Alois P. Heinz (heinz(AT)hs-heilbronn.de), Mar 19 2009
|
| |
|
|
