A025607 Number of n-move rook paths on 8 X 8 board from given corner to same corner.

1, 0, 14, 84, 896, 10080, 127904, 1708224, 23426816, 325032960, 4532831744, 63353816064, 886318555136, 12404650352640, 173642248822784, 2430854346031104, 34031138021113856, 476430995352453120, 6670004313281921024, 93379882656019513344, 1307317290804734590976

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.: (1 - 18*x + 58*x^2)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)).

a(n) = 18*a(n-1) - 44*a(n-2) - 168*a(n-3) for n >= 3. - Andrew Howroyd, Nov 05 2019

Mathematica

CoefficientList[ Series[(1 - 18 x + 58 x^2)/((1 + 2 x) (1 - 6 x) (1 - 14 x)), {x, 0, 16}], x]
LinearRecurrence[{18, -44, -168}, {1, 0, 14}, 30] (* Harvey P. Dale, Feb 13 2023 *)

Prog

(PARI) Vec((1 - 18*x + 58*x^2)/((1 + 2*x)*(1 - 6*x)*(1 - 14*x)) + O(x^20)) \\ Andrew Howroyd, Nov 05 2019

Crossrefs

Cf. A025608, A025609.

Sequence in context: A054149 A273182 A341854 * A272103 A244865 A059600

Adjacent sequences: A025604 A025605 A025606 * A025608 A025609 A025610

Keyword

nonn,easy,walk

Author

David W. Wilson

Extensions

Terms a(17) and beyond from Andrew Howroyd, Nov 05 2019

Status

approved