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Number of ways to place 4 nonattacking wazirs on an n X n board.
11

%I #33 Apr 11 2024 13:57:56

%S 0,0,6,405,5024,31320,133544,446421,1258590,3126724,7042930,14669709,

%T 28658436,53069000,93909924,159819965,262913874,419816676,652912510,

%U 991835749,1475233800,2152832664,3087838016,4359706245,6067321574,8332617060,11304678954

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

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

%H Vincenzo Librandi, <a href="/A172227/b172227.txt">Table of n, a(n) for n = 1..1000</a>

%H J. Brazeal <a href="https://doi.org/10.1080/10724117.2020.1714343">Slides on a Chessboard</a>, Math Horizons, Vol. 27, pp. 24-27, April 2020.

%H Vaclav Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Number of ways of placing non-attacking queens and kings on boards of various sizes</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Fairy_chess_piece">Fairy chess piece</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Wazir_(chess)">Wazir (chess)</a>

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

%F 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

%F a(n) = A232833(n,4). - _R. J. Mathar_, Apr 11 2024

%t 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 *)

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

%K nonn,easy

%O 1,3

%A _Vaclav Kotesovec_, Jan 29 2010

%E Corrected a(3) and g.f., _Vaclav Kotesovec_, Apr 29 2011