A179404 Number of ways to place 3 nonattacking kings on an n X n toroidal board.

0, 0, 0, 48, 600, 3108, 10388, 27328, 61668, 124900, 233288, 409008, 681408, 1088388, 1677900, 2509568, 3656428, 5206788, 7266208, 9959600, 13433448, 17858148, 23430468, 30376128, 38952500, 49451428, 62202168, 77574448, 95981648, 117884100

Offset

1,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

V. Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

Explicit formula: a(n) = 1/6*n^2*(n^4 -27*n^2 +194), n>=4.

G.f.: -4*x^4*(12*x^6 -67*x^5 +140*x^4 -112*x^3 -21*x^2 +66*x +12)/(x-1)^7.

Mathematica

CoefficientList[Series[- 4 x^3 (12 x^6 - 67 x^5 + 140 x^4 - 112 x^3 - 21 x^2 + 66 x + 12) / (x - 1)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 01 2013 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 0, 48, 600, 3108, 10388, 27328, 61668, 124900}, 30] (* Harvey P. Dale, Aug 04 2024 *)

Crossrefs

Cf. A061996, A179403.

Sequence in context: A352847 A042949 A190601 * A171343 A151624 A187611

Adjacent sequences: A179401 A179402 A179403 * A179405 A179406 A179407

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 07 2011

Status

approved