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A172205 Number of ways to place 6 nonattacking kings on a 6 X n board. 3

%I #14 Feb 18 2018 14:59:33

%S 0,0,16,408,8544,62266,291908,1021254,2916232,7179314,15790572,

%T 31795390,59638832,105546666,177953044,287974838,449932632,681918370,

%U 1006409660,1450930734,2048760064,2839684634,3870800868,5197362214,6883673384

%N Number of ways to place 6 nonattacking kings on a 6 X n board.

%H Vincenzo Librandi, <a href="/A172205/b172205.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) = 2*(162n^6-3240n^5+29160n^4-151830n^3+483798n^2-895085n+749335)/5, n>=5.

%F G.f.: -2*x^3*(475*x^8-1015*x^7+4398*x^6+194*x^5+10875*x^4+5233*x^3+3012*x^2 +148*x+8)/(x-1)^7. - _Vaclav Kotesovec_, Mar 24 2010

%t CoefficientList[Series[-2 x^2 (475 x^8 - 1015 x^7 + 4398 x^6 + 194 x^5 + 10875 x^4 + 5233 x^3 + 3012 x^2 + 148 x + 8) / (x - 1)^7, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 27 2013 *)

%Y Cf. A172158, A061992, A172202, A172203, A172204.

%K nonn,easy

%O 1,3

%A _Vaclav Kotesovec_, Jan 29 2010

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)