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 A172135 Number of ways to place 4 nonattacking knights on an n X n board. 11

%I

%S 0,1,18,412,4436,26133,111066,376560,1080942,2732909,6253408,13204356,

%T 26100160,48819677,87137934,149398608,247349946,397168485,620696612,

%U 946921684,1413726108,2069939461,2977725410,4215337872

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

%D E. Bonsdorff, K. Fabel, O. Riihimaa, Schach und Zahl, 1966, p. 51-63

%H Vincenzo Librandi, <a href="/A172135/b172135.txt">Table of n, a(n) for n = 1..1000</a>

%H 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>

%F a(n) = (n^8 - 54n^6 + 144n^5 + 1019n^4 - 5232n^3 - 2022n^2 + 51120n - 77184)/24, n >= 6. (Karl Fabel, 1966)

%F G.f.: -x^2 * (48*x^12 -312*x^11 +690*x^10 -390*x^9 -1162*x^8 +3606*x^7 -5142*x^6 +3099*x^5 -345*x^4 +1292*x^3 +286*x^2 +9*x +1) / (x-1)^9. [_Vaclav Kotesovec_, Mar 25 2010]

%t CoefficientList[Series[-x (48 x^12 - 312 x^11 + 690 x^10 - 390 x^9 - 1162 x^8 + 3606 x^7 - 5142 x^6 + 3099 x^5 - 345 x^4 + 1292 x^3 + 286 x^2 + 9 x + 1) / (x - 1)^9, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 26 2013 *)

%Y Cf. A061994, A172127, A172132, A172134.

%Y Column k=4 of A244081.

%K nonn,easy

%O 1,3

%A _Vaclav Kotesovec_, Jan 26 2010

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Last modified September 25 06:32 EDT 2020. Contains 337335 sequences. (Running on oeis4.)