A201247 Number of ways to place 6 non-attacking ferses on an n X n board.

0, 0, 2, 552, 29412, 527654, 5196928, 34528698, 173951172, 714042302, 2503447216, 7744201834, 21635290132, 55540293510, 132752090192, 298491879178, 636559136340, 1296099575166, 2533344878048, 4774975629082, 8712052571140, 15436347060646, 26634487077600

Offset: 1

Author

Vaclav Kotesovec, Nov 28 2011

Keywords

• nonn
• easy

Comments

Fers is a leaper [1,1].

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• V. Kotesovec, Non-attacking chess pieces, 6ed, p.415
• Index entries for linear recurrences with constant coefficients, signature (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).

Crossrefs

Cf. A176886, A201243, A201244, A201245, A201246, A201248.

Programs

Mathematica

CoefficientList[Series[- 2 x^2 (41 x^14 - 502 x^13 + 2506 x^12 - 7605 x^11 + 18870 x^10 - 41305 x^9 + 60117 x^8 - 21366 x^7 - 73987 x^6 + 52960 x^5 + 237560 x^4 + 93891 x^3 + 11196 x^2 + 263 x + 1)/(x-1)^13, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 30 2013 *)

Formula

a(n) = n^12/720 - 5n^10/48 + n^9/6 + 461n^8/144 - 29n^7/3 - 2147n^6/48 + 1289n^5/6 + 65807n^4/360 - 6356n^3/3 + 9185n^2/6 + 22834n/3 - 11478, n>=5.

G.f.: -2x^3*(41x^14 - 502x^13 + 2506x^12 - 7605x^11 + 18870x^10 - 41305x^9 + 60117x^8 - 21366x^7 - 73987x^6 + 52960x^5 + 237560x^4 + 93891x^3 + 11196x^2 + 263x + 1)/(x-1)^13.