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A172137 Number of ways to place 2 nonattacking zebras on an n X n board.

%I A172137 #26 Aug 01 2022 08:08:38
%S A172137 0,6,36,112,276,582,1096,1896,3072,4726,6972,9936,13756,18582,24576,
%T A172137 31912,40776,51366,63892,78576,95652,115366,137976,163752,192976,
%U A172137 225942,262956,304336,350412,401526,458032,520296,588696,663622,745476,834672,931636,1036806
%N A172137 Number of ways to place 2 nonattacking zebras on an n X n board.
%C A172137 Zebra is a (fairy chess) leaper [2,3].
%D A172137 Christian Poisson, Echecs et mathematiques, Rex Multiplex 29/1990, p. 829.
%H A172137 Vincenzo Librandi, <a href="/A172137/b172137.txt">Table of n, a(n) for n = 1..1000</a>
%H A172137 Vaclav 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 A172137 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A172137 a(n) = (n^4 - 9*n^2 + 40*n - 48)/2, n >= 2. (Christian Poisson, 1990)
%F A172137 G.f.: 2*x^2*(3+3*x-4*x^2+8*x^3-4*x^4)/(1-x)^5. - _Vaclav Kotesovec_, Mar 25 2010
%F A172137 E.g.f.: (1/2)*(16*(3+x) + (-48 + 32*x - 2*x^2 + 6*x^3 + x^4)*exp(x)). - _G. C. Greubel_, Apr 19 2022
%t A172137 CoefficientList[Series[2x(3+3*x-4*x^2+8*x^3-4*x^4)/(1-x)^55, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 26 2013 *)
%o A172137 (Magma) [n eq 1 select 0 else (n^4 -9*n^2 +40*n -48)/2: n in [1..50]]; // _G. C. Greubel_, Apr 19 2022
%o A172137 (SageMath) [(n^4 -9*n^2 +40*n -48 +16*bool(n==1))/2 for n in (1..50)] # _G. C. Greubel_, Apr 19 2022
%Y A172137 Cf. A036464, A172123, A172132.
%K A172137 easy,nonn
%O A172137 1,2
%A A172137 _Vaclav Kotesovec_, Jan 26 2010