|
%I #13 Dec 13 2021 16:09:06
%S 1,9,61,260,927,2578,5965,12066,22135,37678,60457,92488,136043,193650,
%T 268093,362412,479903,624118,798865,1008208,1256467,1548218,1888293,
%U 2281780,2734023,3250622,3837433,4500568,5246395,6081538,7012877
%N Number of ways to place 4 nonattacking bishops on a 4 X n board.
%H Vincenzo Librandi, <a href="/A172208/b172208.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>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).
%F a(n) = (32*n^4 -336*n^3 +1702*n^2 -4701*n +5844) / 3, n>=9.
%F G.f.: -x * (2*x^12 -2*x^11 +4*x^10 -24*x^9 +50*x^8 -10*x^7 +41*x^6 -23*x^5 +152*x^4 +35*x^3 +26*x^2 +4*x+1) / (x-1)^5. - _Vaclav Kotesovec_, Mar 25 2010
%t CoefficientList[Series[-1 (2 x^12 - 2 x^11 + 4 x^10 - 24 x^9 + 50 x^8 - 10 x^7 + 41 x^6 - 23 x^5 + 152 * x^4 + 35 x^3 + 26 x^2 + 4 x + 1) / (x - 1)^5, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 27 2013 *)
%t LinearRecurrence[{5,-10,10,-5,1},{1,9,61,260,927,2578,5965,12066,22135,37678,60457,92488,136043},40] (* _Harvey P. Dale_, Dec 13 2021 *)
%Y Cf. A172127, A061990, A172207.
%K nonn,easy
%O 1,2
%A _Vaclav Kotesovec_, Jan 29 2010
|
