A179427 Number of ways to place 7 nonattacking kings on an n X n toroidal board.

0, 0, 0, 0, 0, 3420, 576856, 19760512, 270487188, 2209065700, 12914201256, 59659859232, 231216019632, 781647658596, 2367858314700, 6553746728448, 16815788711212, 40446802230372, 92003239814224, 199311860224800, 413589922308360, 825997764087012, 1594007700404532, 2982430581363072, 5425904270482500, 9622254525739492, 16669554533555832, 28264133502586912, 46982453295836640, 76676963241363300

Offset

1,6

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 (15, -105, 455, -1365, 3003, -5005, 6435, -6435, 5005, -3003, 1365, -455, 105, -15, 1).

Formula

Explicit formula: a(n) = 1/5040*n^2*(n^12 -189*n^10 +15295*n^8 -681135*n^6 +17692024*n^4 -255655596*n^2 +1617230880), n>=8.

G.f.: -4*x^6*(1379*x^16 - 18219*x^15 + 124755*x^14 - 553765*x^13 + 1657983*x^12 - 3369984*x^11 + 4870575*x^10 - 6400905*x^9 + 10992208*x^8 - 19069951*x^7 + 21246441*x^6 - 8631071*x^5 - 7797385*x^4 + 8273322*x^3 + 2866693*x^2 + 131389*x + 855)/(x-1)^15.

Mathematica

CoefficientList[Series[- 4 x^5 (1379 x^16 - 18219 x^15 + 124755 x^14 - 553765 x^13 + 1657983 x^12 - 3369984 x^11 + 4870575 x^10 - 6400905 x^9 + 10992208 x^8 - 19069951 x^7 + 21246441 x^6 - 8631071 x^5 - 7797385 x^4 + 8273322 x^3 + 2866693 x^2 + 131389 x + 855) / (x - 1)^15, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 01 2013 *)

Crossrefs

Cf. A179403, A179404, A179424, A179425, A179426.

Sequence in context: A109482 A027886 A165942 * A031787 A228674 A268850

Adjacent sequences: A179424 A179425 A179426 * A179428 A179429 A179430

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 07 2011

Status

approved