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%I #38 Apr 15 2022 08:08:51
%S 0,1,16,77,319,920,2397,5278,10874,20355,36390,61171,99441,154882,
%T 235179,346060,499172,702933,974124,1324585,1777555,2349116,3070441,
%U 3962762,5066814,6409975,8044322,10004463,12355749,15141190,18441495,22309336,26843016,32106217
%N Number of inequivalent ways (mod D_4) three checkers can be placed on an n X n board.
%H Erich Friedman, <a href="/A082966/a082966.gif">Illustration of initial terms</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-11,6,14,-14,-6,11,-1,-3,1).
%F a(n) = (1/48)*(n-1)*(n^5+n^4-2*n^3+14*n^2-5*n+3) if n is odd;
%F a(n) = (1/48)*n*(n-1)*(n^2-n+2)*(n^2+2*n-2) if n is even.
%F G.f.: x^2*(x^8-x^7-4*x^6-55*x^5-56*x^4-83*x^3-28*x^2-13*x-1) / ((x-1)^7*(x+1)^4). - _Colin Barker_, Jul 11 2013
%F a(n) = A054247(n, 3) = A054247(n, n^2-3), n >= 1. - _Wolfdieter Lang_, Oct 03 2016
%F E.g.f.: (x*(3 + 24*x + 88*x^2 + 62*x^3 + 15*x^4 + x^5)*cosh(x) + (-3 + 39*x^2 + 80*x^3 + 62*x^4 + 15*x^5 + x^6)*sinh(x))/48. - _Stefano Spezia_, Apr 14 2022
%t Rest@ CoefficientList[Series[x^2*(x^8 - x^7 - 4 x^6 - 55 x^5 - 56 x^4 - 83 x^3 - 28 x^2 - 13 x - 1)/((x - 1)^7*(x + 1)^4), {x, 0, 34}], x] (* _Michael De Vlieger_, Oct 03 2016 *)
%Y Cf. A014409, A054252, A242279, A242358, A054247.
%K nonn,easy
%O 1,3
%A _Vladeta Jovovic_, May 27 2003
%E More terms from _Colin Barker_, Jul 11 2013
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