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A202655 Number of ways to place 4 nonattacking semi-queens on an n X n board. 5

%I

%S 0,0,0,7,223,2429,15045,66122,230074,675798,1745318,4073993,8764753,

%T 17630795,33522531,60756612,105666148,177293340,288246972,455749371,

%U 702898611,1060173961,1567213681,2274896558,3247759614,4566786770,6332604226,8669120733,11727651845

%N Number of ways to place 4 nonattacking semi-queens on an n X n board.

%C Two semi-queens do not attack each other if they are in the same northwest-southeast diagonal.

%H Michael De Vlieger, <a href="/A202655/b202655.txt">Table of n, a(n) for n = 1..10000</a>

%H Christopher R. H. Hanusa, Thomas Zaslavsky, <a href="https://arxiv.org/abs/1906.08981">A q-queens problem. VII. Combinatorial types of nonattacking chess riders</a>, arXiv:1906.08981 [math.CO], 2019.

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>

%F a(n) = n^8/24 - 2*n^7/3 + 41*n^6/9 - 257*n^5/15 + 341*n^4/9 - 97*n^3/2 + 2341*n^2/72 - 87*n/10 + (n/2 - 1/2)*floor(n/2).

%F G.f.: -x^4*(151*x^6 + 1022*x^5 + 2233*x^4 + 2132*x^3 + 1001*x^2 + 174*x + 7)/((x-1)^9*(x+1)^2).

%t Rest@ CoefficientList[Series[-x^4*(151 x^6 + 1022 x^5 + 2233 x^4 + 2132 x^3 + 1001 x^2 + 174 x + 7)/((x - 1)^9*(x + 1)^2), {x, 0, 29}], x] (* _Michael De Vlieger_, Aug 19 2019 *)

%Y Cf. A099152, A061994, A103220, A202654, A202656, A202657.

%K nonn

%O 1,4

%A _Vaclav Kotesovec_, Dec 22 2011

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Last modified August 10 06:08 EDT 2022. Contains 356029 sequences. (Running on oeis4.)