%I #26 Jan 27 2025 14:46:12
%S 0,0,38,340,1630,5552,15210,35828,75530,146240,264702,453620,742918,
%T 1171120,1786850,2650452,3835730,5431808,7545110,10301460,13848302,
%U 18357040,24025498,31080500,39780570,50418752,63325550,78871988,97472790,119589680,145734802
%N Number of ways to place 3 non-attacking ferses on an n X n board.
%C Fers is a leaper [1,1].
%H Vincenzo Librandi, <a href="/A201244/b201244.txt">Table of n, a(n) for n = 1..1000</a>
%H Vaclav Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, p.415
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F a(n) = (n-2)*(n^5 + 2n^4 - 11n^3 + 2n^2 + 54n - 60)/6, n>=2.
%F G.f.: -2x^3*(x^5 + 3x^4 - 24x^3 + 24x^2 + 37x + 19)/(x-1)^7.
%F a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7). - _Vincenzo Librandi_, Apr 30 2013
%t CoefficientList[Series[- 2 x^2 (x^5 + 3 x^4 - 24 x^3 + 24 x^2 + 37 x + 19) / (x-1)^7, {x, 0, 40}], x] (* _Vincenzo Librandi_, Apr 30 2013 *)
%o (Magma) I:=[0, 0, 38, 340, 1630, 5552, 15210, 35828]; [n le 8 select I[n] else 7*Self(n-1)-21*Self(n-2)+35*Self(n-3)-35*Self(n-4)+21*Self(n-5)-7*Self(n-6)+Self(n-7): n in [1..40]]; // _Vincenzo Librandi_, Apr 30 2013
%o (Magma) [0] cat [(n-2)*(n^5+2*n^4-11*n^3 +2*n^2+54*n-60)/6: n in [2..35]]; // _Vincenzo Librandi_, Apr 30 2013
%Y Cf. A172124, A201243, A201245, A201246, A201247, A201248.
%K nonn,easy
%O 1,3
%A _Vaclav Kotesovec_, Nov 28 2011