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A025608 Number of n-move rook paths on 8 X 8 board from given corner to opposite corner. 3
0, 0, 2, 36, 560, 8160, 116192, 1638336, 23006720, 322513920, 4517714432, 63263118336, 885774356480, 12401385185280, 173622657769472, 2430736799809536, 34030432743587840, 476426763687690240, 6669978923292557312, 93379730316084903936, 1307316376765123788800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Paths are not required to be self-avoiding. - Andrew Howroyd, Nov 05 2019

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (18,-44,-168).

FORMULA

G.f.: (2*x^2)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)).

a(0)=0, a(1)=0, a(2)=2, a(n)=18*a(n-1)-44*a(n-2)-168*a(n-3). - Harvey P. Dale, Mar 09 2013

MATHEMATICA

CoefficientList[Series[(2x^2)/((1+2x)(1-6x)(1-14x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{18, -44, -168}, {0, 0, 2}, 30] (* Harvey P. Dale, Mar 09 2013 *)

PROG

(PARI) concat([0, 0], Vec(2/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)) + O(x^20))) \\ Andrew Howroyd, Nov 05 2019

CROSSREFS

Cf. A025607, A025609.

Sequence in context: A092852 A139738 A248343 * A230132 A141132 A064030

Adjacent sequences:  A025605 A025606 A025607 * A025609 A025610 A025611

KEYWORD

nonn,walk

AUTHOR

David W. Wilson

EXTENSIONS

More terms from Harvey P. Dale, Mar 09 2013

STATUS

approved

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Last modified September 24 06:13 EDT 2021. Contains 347623 sequences. (Running on oeis4.)