A178409 Number of ways to place 6 nonattacking wazirs on an n X n board.

0, 0, 0, 114, 14650, 368868, 4216498, 30222074, 158918030, 669582340, 2387463550, 7470004954, 21036576578, 54315955588, 130382565930, 294116445082, 628800849110, 1282821452132, 2511317339446, 4739431178170

Offset: 1

Author

Vaclav Kotesovec, May 27 2010

Keywords

• nonn
• easy

Comments

Wazir is a (fairy chess) leaper [0,1].

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• V. Kotesovec, Non-attacking chess pieces, 6ed, 2013

Crossrefs

Cf. A172225, A172226, A172227, A172228.

Programs

Mathematica

CoefficientList[Series[- 2 x^3 (4 x^13 - 17 x^12 + 3 x^11 - 469 x^10 + 4084 x^9 - 10233 x^8 - 3482 x^7 + 66494 x^6 - 125152 x^5 + 35457 x^4 + 265655 x^3 + 93655 x^2 + 6584 x + 57) / (x - 1)^13, {x, 0, 50}], x] (* Vincenzo Librandi, May 31 2013 *)

Formula

Explicit formula: a(n) = 1/720 * (n^12 -75*n^10 +60*n^9 +2365*n^8 -3720*n^7 -38085*n^6 +89580*n^5 +292834*n^4 -984960*n^3 -552240*n^2 +4128960*n -3160800), n >= 5.

G.f.: -2*x^4 * (4*x^13 -17*x^12 +3*x^11 -469*x^10 +4084*x^9 -10233*x^8 -3482*x^7 +66494*x^6 -125152*x^5 +35457*x^4 +265655*x^3 +93655*x^2 +6584*x +57)/(x-1)^13.

a(n) = A232833(n,6). - R. J. Mathar, Apr 11 2024