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A201243 Number of ways to place 2 non-attacking ferses on an n X n board.

%I A201243 #29 Jan 21 2025 17:23:22
%S A201243 0,4,28,102,268,580,1104,1918,3112,4788,7060,10054,13908,18772,24808,
%T A201243 32190,41104,51748,64332,79078,96220,116004,138688,164542,193848,
%U A201243 226900,264004,305478,351652,402868,459480,521854,590368,665412,747388,836710,933804,1039108
%N A201243 Number of ways to place 2 non-attacking ferses on an n X n board.
%C A201243 Fers is a leaper [1,1].
%H A201243 Vincenzo Librandi, <a href="/A201243/b201243.txt">Table of n, a(n) for n = 1..1000</a>
%H A201243 Vaclav Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, p.415
%H A201243 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A201243 a(n) = 1/2*(n-1)*(n^3 + n^2 - 4n + 4) by C. Poisson, 1990.
%F A201243 G.f.: 2x^2*(x+1)*(x^2-2x-2)/(x-1)^5.
%F A201243 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 A201243 Table[(n - 1) (n^3 + n^2 - 4 n + 4) / 2, {n, 100}] (* _Vincenzo Librandi_, Apr 30 2013 *)
%t A201243 LinearRecurrence[{5,-10,10,-5,1},{0,4,28,102,268},40] (* _Harvey P. Dale_, Dec 31 2014 *)
%o A201243 (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]]; // _Vincenzo Librandi_, Apr 30 2013
%o A201243 (Magma) [(n-1)*(n^3+n^2-4*n+4)/2: n in [1..40]]; // _Vincenzo Librandi_, Apr 30 2013
%Y A201243 Cf. A172123, A201244, A201245, A201246, A201247, A201248.
%K A201243 nonn,easy
%O A201243 1,2
%A A201243 _Vaclav Kotesovec_, Nov 28 2011