A025608 Number of n-move rook paths on 8 X 8 board from given corner to opposite corner.

0, 0, 2, 36, 560, 8160, 116192, 1638336, 23006720, 322513920, 4517714432, 63263118336, 885774356480, 12401385185280, 173622657769472, 2430736799809536, 34030432743587840, 476426763687690240, 6669978923292557312, 93379730316084903936, 1307316376765123788800

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