A158450 Number of spanning forests in 3 X n grid.

1, 4, 112, 3102, 85818, 2373870, 65664106, 1816344222, 50242141946, 1389754592846, 38442187035914, 1063354458854270, 29413589398458778, 813613216256931886, 22505463603889302698, 622526628016224886878, 17219792020736937982522, 476318961941184616298510

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..250

Index entries for linear recurrences with constant coefficients, signature (33,-154,176,-32).

Formula

G.f.: (28*x^4-154*x^3+134*x^2-29*x+1)/(32*x^4-176*x^3+154*x^2-33*x+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-> ceil((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=0..20);

Crossrefs

Row 3 of A360194.

Sequence in context: A181485 A135917 A241798 * A063406 A361543 A221625

Adjacent sequences: A158447 A158448 A158449 * A158451 A158452 A158453

Keyword

nonn,easy

Author

Alois P. Heinz, Mar 19 2009

Extensions

a(0) inserted by Alois P. Heinz, Jan 23 2013

Status

approved