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A240445 Numbers of ways to place five indistinguishable points on an n X n square grid so that no four of them are vertices of a square of any orientation.

%I A240445 #19 Feb 09 2024 11:16:02
%S A240445 96,4128,52080,373632,1898064,7604352,25580016,75208320,198651024,
%T A240445 480768288,1081848768,2289041664,4594218720,8808178176,16223664672,
%U A240445 28842649344,49686723072,83213333280,135864971088,216783321216,338725852080,519228378240,782063802000
%N A240445 Numbers of ways to place five indistinguishable points on an n X n square grid so that no four of them are vertices of a square of any orientation.
%C A240445 All elements of the sequence are multiples of 48.
%H A240445 Heinrich Ludwig, <a href="/A240445/b240445.txt">Table of n, a(n) for n = 3..1000</a>
%H A240445 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F A240445 a(n) = (n^10 - 10*n^8 + 25*n^6 - 16*n^2)/120.
%F A240445 G.f.: -48*x^3*(x+1)*(2*x^4+62*x^3+187*x^2+62*x+2) / (x-1)^11. - _Colin Barker_, May 09 2014
%p A240445 A240445:=n->(n^10 - 10*n^8 + 25*n^6 - 16*n^2)/120; seq(A240445(n), n=3..30); # _Wesley Ivan Hurt_, May 09 2014
%t A240445 Table[(n^10 - 10*n^8 + 25*n^6 - 16*n^2)/120, {n, 3, 30}] (* _Wesley Ivan Hurt_, May 09 2014 *)
%o A240445 (Magma) [(n^10 - 10*n^8 + 25*n^6 - 16*n^2)/120: n in [3..30]]; // _Wesley Ivan Hurt_, May 09 2014
%Y A240445 Cf. A240444, A240446.
%K A240445 nonn,easy
%O A240445 3,1
%A A240445 _Heinrich Ludwig_, May 09 2014