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%I #21 Apr 23 2023 22:26:47
%S 0,0,0,0,2,12,46,140,344,732,1400,2468,4080,6404,9632,13980,19688,
%T 27020,36264,47732,61760,78708,98960,122924,151032,183740,221528,
%U 264900,314384,370532,433920,505148,584840,673644,772232,881300,1001568,1133780,1278704,1437132
%N Number of ways to place 4 nonattacking queens on a 4 X n board.
%H Vincenzo Librandi, <a href="/A061990/b061990.txt">Table of n, a(n) for n = 0..1000</a>
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Ways of placing non-attacking queens and kings...</a>, part of "Between chessboard and computer", 1996, pp. 204 - 206.
%H E. Lucas, <a href="http://gallica.bnf.fr/ark:/12148/bpt6k3943s/f256.image.r=">Recreations mathematiques I</a>, Albert Blanchard, Paris, 1992, p. 231.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F G.f.: -2*x^4*(x^3-x^2+x+1)*(x^4+4*x^2+1)/(x-1)^5.
%F Recurrence: a(n)=5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5), n >= 12.
%F Explicit formula (H. Tarry, 1890): a(n)=n^4-18*n^3+139*n^2-534*n+840, n >= 7.
%t Join[{0,0,0,0,2,12,46},LinearRecurrence[{5,-10,10,-5,1},{140,344,732,1400,2468},30]] (* _Harvey P. Dale_, Mar 06 2013 *)
%t CoefficientList[Series[-2 x^4 (x^3 - x^2 + x + 1) (x^4 + 4 x^2 + 1) / (x-1)^5, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 02 2013 *)
%o (PARI) a(n)=if(n<7,[0, 0, 0, 0, 2, 12, 46][n+1],n^4-18*n^3+139*n^2-534*n+840) \\ _Charles R Greathouse IV_, Oct 21 2022
%Y Cf. A061989.
%K nonn,easy
%O 0,5
%A Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), May 29 2001
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