%I #22 Sep 08 2022 08:46:01

%S 0,4,28,102,268,580,1104,1918,3112,4788,7060,10054,13908,18772,24808,

%T 32190,41104,51748,64332,79078,96220,116004,138688,164542,193848,

%U 226900,264004,305478,351652,402868,459480,521854,590368,665412,747388,836710,933804,1039108

%N Number of ways to place 2 non-attacking ferses on an n X n board.

%C Fers is a leaper [1,1].

%H Vincenzo Librandi, <a href="/A201243/b201243.txt">Table of n, a(n) for n = 1..1000</a>

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, p.415

%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) = 1/2*(n-1)*(n^3 + n^2 - 4n + 4) by C. Poisson, 1990.

%F G.f.: 2x^2*(x+1)*(x^2-2x-2)/(x-1)^5.

%F a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - _Vincenzo Librandi_, Apr 30 2013

%t Table[(n - 1) (n^3 + n^2 - 4 n + 4) / 2, {n, 100}] (* _Vincenzo Librandi_, Apr 30 2013 *)

%t LinearRecurrence[{5,-10,10,-5,1},{0,4,28,102,268},40] (* _Harvey P. Dale_, Dec 31 2014 *)

%o (Magma) I:=[0, 4, 28, 102, 268]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..40]]; /* or */ [(n-1)*(n^3+n^2-4*n+4)/2: n in [1..40]]; // _Vincenzo Librandi_, Apr 30 2013

%Y Cf. A172123, A201244, A201245, A201246, A201247, A201248.

%K nonn,easy

%O 1,2

%A _Vaclav Kotesovec_, Nov 28 2011