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A025607 Number of n-move rook paths on 8 X 8 board from given corner to same corner. 3
1, 0, 14, 84, 896, 10080, 127904, 1708224, 23426816, 325032960, 4532831744, 63353816064, 886318555136, 12404650352640, 173642248822784, 2430854346031104, 34031138021113856, 476430995352453120, 6670004313281921024, 93379882656019513344, 1307317290804734590976 (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.: (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]

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

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Last modified October 4 01:04 EDT 2022. Contains 357237 sequences. (Running on oeis4.)