|
%I #19 Apr 23 2023 22:27:06
%S 1,6,26,86,211,426,758,1234,1881,2726,3796,5118,6719,8626,10866,13466,
%T 16453,19854,23696,28006,32811,38138,44014,50466,57521,65206,73548,
%U 82574,92311,102786,114026,126058,138909,152606,167176,182646,199043,216394,234726,254066
%N Number of ways to place 3 nonattacking bishops on a 3 X n board.
%H Vincenzo Librandi, <a href="/A172207/b172207.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_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = (9n^3 - 45n^2 + 106n - 108)/2, n>=4.
%F G.f.: x*(2*x^6+14*x^3+8*x^2+2*x+1)/(x-1)^4. - _Vaclav Kotesovec_, Mar 25 2010
%t CoefficientList[Series[(2 x^6 + 14 x^3 + 8 x^2 + 2 x + 1) / (x - 1)^4, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 27 2013 *)
%Y Cf. A172124, A061989, A047659, A061996.
%K nonn,easy
%O 1,2
%A _Vaclav Kotesovec_, Jan 29 2010
|
