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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Paths are self-avoiding 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) ~ ((3/4-sqrt(13)/52)*n-1/4-sqrt(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

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Last modified December 7 09:33 EST 2019. Contains 329843 sequences. (Running on oeis4.)