A025592 Number of n-move bishop paths on 8x8 board from given corner to any square.

1, 7, 73, 687, 6433, 59671, 550873, 5070495, 46587505, 427571527, 3921497065, 35951032335, 329500954945, 3019471143415, 27666914986873, 253491202255359, 2322457297730449, 21277556849745703, 194934635068180105

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (22,-166,468,-113,-1066,184,192).

Formula

G.f.: (-120*x^5 + 274*x^4 - 225*x^3 + 85*x^2 - 15*x + 1)/(-192*x^7 - 184*x^6 + 1066*x^5 + 113*x^4 - 468*x^3 + 166*x^2 - 22*x + 1)

Mathematica

LinearRecurrence[{22, -166, 468, -113, -1066, 184, 192}, {1, 7, 73, 687, 6433, 59671, 550873}, 30] (* Harvey P. Dale, Dec 28 2021 *)

Prog

(PARI) a(n)=([0, 1, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 1; 192, 184, -1066, -113, 468, -166, 22]^n*[1; 7; 73; 687; 6433; 59671; 550873])[1, 1] \\ Charles R Greathouse IV, Jun 01 2026

Crossrefs

Sequence in context: A050917 A308418 A240195 * A009142 A386293 A155614

Adjacent sequences: A025589 A025590 A025591 * A025593 A025594 A025595

Keyword

nonn,easy

Author

David W. Wilson

Status

approved