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A172224 Number of ways to place 6 nonattacking zebras on a 6 X n board.

%I A172224 #20 Feb 16 2025 08:33:11
%S A172224 1,924,8989,37270,145233,525796,1605490,4136952,9435413,19632414,
%T A172224 37957424,69050898,119351315,197524064,314935542,486171662,729604121,
%U A172224 1068003424,1529198580,2146783422,2960869583,4018886128,5376425842
%N A172224 Number of ways to place 6 nonattacking zebras on a 6 X n board.
%C A172224 Zebra is a (fairy chess) leaper [2,3].
%H A172224 Vincenzo Librandi, <a href="/A172224/b172224.txt">Table of n, a(n) for n = 1..1000</a>
%H A172224 V. 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 A172224 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ZebraGraph.html.html">Zebra Graph</a>
%H A172224 Wikipedia, <a href="https://en.wikipedia.org/wiki/Zebra_(chess)">Zebra (chess)</a>
%F A172224 a(n) = (1944n^6-27540n^5+227070n^4-1222555n^3+4366071n^2-9580580n+9925860)/30, n>=15.
%F A172224 For any fixed value of k > 1, a(n) = 1/k!*(kn)^k - (k-1)(9k-20)/2/k!*(kn)^(k-1) + ...
%F A172224 G.f.: -x * (32*x^20 -48*x^19 -84*x^18 -1004*x^17 +3350*x^16 -802*x^15 +3364*x^14 -32132*x^13 +42540*x^12 +3538*x^11 +10674*x^10 -126767*x^9 +151663*x^8 -20769*x^7 -34421*x^6 +9539*x^5 +40807*x^4 -6284*x^3 +2542*x^2 +917*x +1) / (x-1)^7. - _Vaclav Kotesovec_, Mar 25 2010
%t A172224 CoefficientList[Series[-(32 x^20 - 48 x^19 - 84 x^18 - 1004 x^17 + 3350 x^16 - 802 x^15 + 3364 x^14 - 32132 x^13 + 42540 x^12 + 3538 x^11 + 10674 x^10 - 126767 x^9 + 151663 x^8 - 20769 x^7 - 34421 x^6 + 9539 x^5 + 40807 x^4 - 6284 x^3 + 2542 x^2 + 917 x + 1) / (x - 1)^7, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 28 2013 *)
%Y A172224 Cf. A061992, A172221, A172222, A172223.
%K A172224 nonn,easy
%O A172224 1,2
%A A172224 _Vaclav Kotesovec_, Jan 29 2010