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A172214 Number of ways to place 5 nonattacking knights on a 5 X n board. 5

%I #17 Feb 18 2018 15:01:23

%S 1,28,259,1968,9386,30842,82738,192336,400277,763984,1360797,2291056,

%T 3681226,5687022,8496534,12333352,17459691,24179516,32841667,43842984,

%U 57631432,74709226,95635956,121031712,151580209

%N Number of ways to place 5 nonattacking knights on a 5 X n board.

%H Vincenzo Librandi, <a href="/A172214/b172214.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) = (625n^5-8250n^4+57235n^3-242778n^2+608440n-705984)/24, n>=8.

%F G.f.: x * (42*x^12 -52*x^11 -268*x^10 +884*x^9 -268*x^8 -1188*x^7 +2834*x^6 -720*x^5 +918*x^4 +814*x^3 +106*x^2 +22*x +1) / (x-1)^6. - _Vaclav Kotesovec_, Mar 25 2010

%t CoefficientList[Series[(42 x^12 - 52 x^11 - 268 x^10 + 884 x^9 - 268 x^8 - 1188 x^7 + 2834 x^6 - 720 x^5 + 918 x^4 + 814 x^3 + 106 x^2 + 22 x + 1) / (x - 1)^6, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 27 2013 *)

%Y Cf. A172136, A061991, A172212, A172213.

%K nonn,easy

%O 1,2

%A _Vaclav Kotesovec_, Jan 29 2010

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Last modified March 28 16:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)