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Number of ways to place 4 nonattacking zebras on an n X n board.
5

%I #16 Apr 19 2022 04:38:55

%S 0,1,126,1168,7334,35749,137970,438984,1208246,2969389,6662480,

%T 13873100,27144408,50389581,89424014,152638280,251834530,403250693,

%U 628798516,957543164,1427453780,2087456085,2999819778,4242915176

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

%C Zebra is a (fairy chess) leaper [2,3].

%H Vincenzo Librandi, <a href="/A172139/b172139.txt">Table of n, a(n) for n = 1..1000</a>

%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 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).

%F a(n) = (n^8 - 54*n^6 + 240*n^5 + 827*n^4 - 8592*n^3 + 10362*n^2 + 75600*n - 204864)/24, n >= 9.

%F G.f.: x^2*(1 + 117*x + 70*x^2 + 1274*x^3 + 1333*x^4 - 2109*x^5 - 462*x^6 + 8858*x^7 - 17006*x^8 + 15166*x^9 - 6838*x^10 + 1478*x^11 - 650*x^12 + 760*x^13 - 376*x^14 + 64*x^15)/(1-x)^9. - _Vaclav Kotesovec_, Mar 25 2010

%t CoefficientList[Series[x(1+117*x+70*x^2+1274*x^3+1333*x^4-2109*x^5-462*x^6 +8858*x^7-17006*x^8+15166*x^9-6838*x^10+1478*x^11-650*x^12+760*x^13-376*x^14 +64*x^15)/(1-x)^9, {x,0,40}], x] (* _Vincenzo Librandi_, May 27 2013 *)

%o (SageMath) [0,1,126,1168,7334,35749,137970,438984] + [(n^8 -54*n^6 +240*n^5 +827*n^4 -8592*n^3 +10362*n^2 +75600*n -204864)/24 for n in (9..50)] # _G. C. Greubel_, Apr 19 2022

%Y Cf. A061994, A172127, A172135, A172137, A172138.

%K nonn

%O 1,3

%A _Vaclav Kotesovec_, Jan 26 2010