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A176886 Number of ways to place 6 nonattacking bishops on an n X n board. 9

%I #14 Aug 23 2017 12:58:14

%S 0,0,0,16,1960,53744,692320,5599888,33001664,154215760,603563504,

%T 2052729728,6229649352,17202203680,43870041520,104531112928,

%U 234870173248,501360888160

%N Number of ways to place 6 nonattacking bishops on an n X n board.

%H Vincenzo Librandi, <a href="/A176886/b176886.txt">Table of n, a(n) for n = 1..1000</a>

%H Christopher R. H. Hanusa, T Zaslavsky, S Chaiken, <a href="http://arxiv.org/abs/1609.00853">A q-Queens Problem. IV. Queens, Bishops, Nightriders (and Rooks)</a>, arXiv preprint arXiv:1609.00853, a12016

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013

%F From _Vaclav Kotesovec_, Apr 27 2010: (Start)

%F Explicit formula: a(n) = n*(n-2)*(126*n^10 -2268*n^9 +18774*n^8 -97216*n^7 +361165*n^6 -1029454*n^5 +2283178*n^4 -3841960*n^3 +4676932*n^2 -3808152*n +1640160)/90720 if n is even and a(n) = (n-1)*(n-3)*(126*n^10 -2016*n^9 +14868*n^8 -69244*n^7 +234017*n^6 -607984*n^5 +1211879*n^4 -1797328*n^3 +1953593*n^2 -1550820*n +722925)/90720 if n is odd.

%F G.f.: -8x^4*(90x^15 +1332x^14 +15417x^13 +93042x^12 +372376x^11 +983864x^10 +1834807x^9 +2423054x^8 +2310242x^7 +1568260x^6 +748519x^5 +239742x^4 +48236x^3 +5264x^2 +233x +2)/((x-1)^13*(x+1)^7). (End)

%t CoefficientList[Series[- 8 x^3 (90 x^15 + 1332 x^14 + 15417 x^13 + 93042 x^12 + 372376 x^11 + 983864 x^10 + 1834807 x^9 + 2423054 x^8 + 2310242 x^7 + 1568260 x^6 + 748519 x^5 + 239742 x^4 + 48236 x^3 + 5264 x^2 + 233 x + 2) / ((x - 1)^13 (x + 1)^7), {x, 0, 50}], x] (* _Vincenzo Librandi_, May 31 2013 *)

%Y Cf. A172123, A172124, A172127, A172129.

%K nonn,easy

%O 1,4

%A _Vaclav Kotesovec_, Apr 28 2010

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