A194652 Number of ways to place 4 nonattacking kings on an n X n cylindrical chessboard.

0, 0, 0, 32, 1205, 13260, 74494, 291708, 908973, 2416410, 5711530, 12327414, 24743693, 46797968, 84216990, 145288600, 241697109, 389546478, 610597338, 933745570, 1396771845, 2048393204, 2950649438, 4181658708, 5838778525, 8042209890, 10939084074, 14708073198

Offset

1,4

Links

Table of n, a(n) for n=1..28.

V. Kotesovec, Number of ways of placing non-attacking queens, kings, bishops and knights

Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

Formula

a(n) = 1/24*n*(n^7 - 54*n^5 + 36*n^4 + 1019*n^3 - 1236*n^2 - 6690*n + 10884), n>=5.

G.f.: x^4*(54*x^9 - 384*x^8 + 1052*x^7 - 1263*x^6 + 657*x^5 - 1434*x^4 + 4154*x^3 - 3567*x^2 - 917*x - 32)/(x-1)^9.

Mathematica

CoefficientList[Series[x^3*(54*x^9 - 384*x^8 + 1052*x^7 - 1263*x^6 + 657*x^5 - 1434*x^4 + 4154*x^3 - 3567*x^2 - 917*x - 32)/(x - 1)^9, {x, 0, 30}], x] (* Wesley Ivan Hurt, Dec 27 2023 *)

Crossrefs

Cf. A061997, A179424, A194650, A194651.

Sequence in context: A318014 A320400 A367538 * A330481 A240892 A241107

Adjacent sequences: A194649 A194650 A194651 * A194653 A194654 A194655

Keyword

nonn

Author

Vaclav Kotesovec, Aug 31 2011

Status

approved