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A321251 a(n) is the number of ways to place non-attacking knights on a 3 X n chessboard.

%I A321251 #28 Nov 06 2018 13:22:10
%S A321251 1,8,36,94,278,1062,3650,11856,39444,135704,456980,1534668,5166204,
%T A321251 17480600,58888528,198548648,669291696,2258436248,7613387344,
%U A321251 25676313144,86575342536,291991130840,984557555352,3320284572360,11196209499736,37757232570616
%N A321251 a(n) is the number of ways to place non-attacking knights on a 3 X n chessboard.
%C A321251 For n = 3, a(3) = 94 is the same as A141243(3). In both cases these are 3 X 3 chessboards.
%H A321251 Dimitrios Noulas, <a href="/A321251/b321251.txt">Table of n, a(n) for n = 0..1000</a>
%H A321251 V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013, p. 297-301.
%F A321251 G.f.: -(36*x^15 - 72*x^14 - 60*x^13 + 72*x^12 - 120*x^11 + 250*x^10 + 270*x^9 - 256*x^8 - 30*x^7 - 78*x^6 - 98*x^5 + 92*x^4 + 36*x^3 - 8*x^2 - 5*x - 1)/(36*x^16 - 108*x^15 + 48*x^14 + 24*x^13 - 144*x^12 + 376*x^11 - 70*x^10 - 174*x^9 + 108*x^8 - 168*x^7 + 26*x^6 + 78*x^5 - 24*x^4 + 10*x^3 - 4*x^2 - 3*x + 1).
%t A321251 CoefficientList[Series[-(36 x^15 - 72 x^14 - 60 x^13 + 72 x^12 - 120 x^11 + 250 x^10 + 270 x^9 - 256 x^8 - 30 x^7 - 78 x^6 - 98 x^5 + 92 x^4 + 36 x^3 - 8 x^2 - 5 x - 1)/(36 x^16 - 108 x^15 + 48 x^14 + 24 x^13 - 144 x^12 + 376 x^11 - 70 x^10 - 174 x^9 + 108 x^8 - 168 x^7 + 26 x^6 + 78 x^5 - 24 x^4 + 10 x^3 - 4 x^2 - 3 x + 1), {x, 0, 25}], x] (* _Michael De Vlieger_, Nov 05 2018 *)
%o A321251 (Sage) G(x)=-(36*x^15 - 72*x^14 - 60*x^13 + 72*x^12 - 120*x^11 + 250*x^10 + 270*x^9 - 256*x^8 - 30*x^7 - 78*x^6 - 98*x^5 + 92*x^4 + 36*x^3 - 8*x^2 - 5*x - 1)/(36*x^16 - 108*x^15 + 48*x^14 + 24*x^13 - 144*x^12 + 376*x^11 - 70*x^10 - 174*x^9 + 108*x^8 - 168*x^7 + 26*x^6 + 78*x^5 - 24*x^4 + 10*x^3 - 4*x^2 - 3*x + 1)
%o A321251 G.series(x,1001)
%Y A321251 Cf. A141243, A189145.
%K A321251 nonn,easy
%O A321251 0,2
%A A321251 _Dimitrios Noulas_, Nov 01 2018