A172227 Number of ways to place 4 nonattacking wazirs on an n X n board.

0, 0, 6, 405, 5024, 31320, 133544, 446421, 1258590, 3126724, 7042930, 14669709, 28658436, 53069000, 93909924, 159819965, 262913874, 419816676, 652912510, 991835749, 1475233800, 2152832664, 3087838016, 4359706245, 6067321574, 8332617060, 11304678954

Offset: 1

Author

Vaclav Kotesovec, Jan 29 2010

Keywords

• nonn
• easy

Comments

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• J. Brazeal Slides on a Chessboard, Math Horizons, Vol. 27, pp. 24-27, April 2020.
• Vaclav Kotesovec, Number of ways of placing non-attacking queens and kings on boards of various sizes
• Eric Weisstein's World of Mathematics, Grid Graph
• Wikipedia, Fairy chess piece
• Wikipedia, Wazir (chess)

Crossrefs

Cf. A172225, A172226, A061994, A061997, A172127, A172135, A172139, A006506.

Programs

Mathematica

CoefficientList[Series[- x^2 (4 x^8 - 26 x^7 + 3 x^6 + 303 x^5 - 736 x^4 + 180 x^3 + 1595 x^2 + 351 x + 6) / (x - 1)^9, {x, 0, 50}], x] (* Vincenzo Librandi, May 28 2013 *)

Formula

a(n) = (n^8-30n^6+24n^5+323n^4-504n^3-1110n^2+2760n-1224)/24, n>=3.

G.f.: -x^3*(4*x^8-26*x^7+3*x^6+303*x^5-736*x^4+180*x^3+1595*x^2+351*x+6)/(x-1)^9. - Vaclav Kotesovec, Apr 29 2011

a(n) = A232833(n,4). - R. J. Mathar, Apr 11 2024

Extensions

Corrected a(3) and g.f., Vaclav Kotesovec, Apr 29 2011