

A181394


Summed lengths of all nonintersecting rook paths on a 3 x n board.


6



2, 14, 64, 284, 1206, 4882, 19060, 72588, 271548, 1001964, 3656480, 13223348, 47461350, 169263658, 600355808, 2119297852, 7450253362, 26095036854, 91102304600, 317127751352, 1101029901244, 3813576283628, 13180379580636, 45463936339816
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OFFSET

1,1


COMMENTS

Paths are selfavoiding from one corner to the diagonally opposite corner.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000


FORMULA

G.f.: (4*x^6 4*x^5 +4*x^4 24*x^3 +4*x^2 +2*x 2)*x / (x^8 +4*x^7 2*x^6 4*x^5 +23*x^4 28*x^3 +22*x^2 8*x +1).  Alois P. Heinz, Nov 26 2010
Asymptotics: a(n) ~ ((3/4sqrt(13)/52)*n1/4sqrt(13)/52)*((sqrt(13)+3)/2)^n [From Vaclav Kotesovec, Aug 31 2012]


EXAMPLE

E.g. s(2) {RRD, DRR, RDR, DRURD} 3+3+3+5 = 14.


MAPLE

a:= n> (Matrix(8, (i, j)>if i+1=j then 1 elif i=8 then [1, 4, 2, 4, 23, 28, 22, 8][j] else 0 fi)^n. <<0, 2, 14, 64, 284, 1206, 4882, 19060>>)[1, 1]: seq (a(n), n=1..24); # Alois P. Heinz, Nov 26 2010


CROSSREFS

Enumeration of these paths is A006192, related sequences A181395, A181396, A181397, A181398, A181399.
Sequence in context: A144657 A167555 A222445 * A266590 A196977 A254197
Adjacent sequences: A181391 A181392 A181393 * A181395 A181396 A181397


KEYWORD

nonn,walk


AUTHOR

David Scambler, Oct 17 2010


EXTENSIONS

More terms from Alois P. Heinz, Nov 26 2010


STATUS

approved



