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A279439 Number of ways to place 5 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

%I A279439 #16 Dec 23 2016 21:44:01
%S A279439 0,0,45,2304,34020,270720,1475145,6209280,21654864,65422080,176467005,
%T A279439 434206080,990140580,2117816064,4288771305,8284308480,15355471680,
%U A279439 27446584320,47501098029,79872376320,130866406020,209448328320,328150139625,504222960384,761083938000
%N A279439 Number of ways to place 5 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.
%C A279439 Column 6 of triangle A279445.
%C A279439 Rotations and reflections of placements are counted. For numbers if they are to be ignored see A279449.
%C A279439 For condition "no more than 2 points on straight lines at any angle", see A194190.
%H A279439 Heinrich Ludwig, <a href="/A279439/b279439.txt">Table of n, a(n) for n = 1..1000</a>
%H A279439 <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 A279439 a(n) = (n^10 -30*n^8 +90*n^7 -27*n^6 -270*n^5 +500*n^4 -360*n^3 +96*n^2)/120.
%F A279439 a(n) = 11*a(n-1) -55*a(n-2) +165*a(n-3) -330*a(n-4) +462*a(n-5) -462*a(n-6) +330*a(n-7) -165*a(n-8) +55*a(n-9) -11*a(n-10) +*a(n-11).
%F A279439 G.f.: 9*x^3*(5 +201*x +1239*x^2 +1755*x^3 +335*x^4 -165*x^5 -11*x^6 +x^7) / (1 -x)^11. - _Colin Barker_, Dec 22 2016
%t A279439 Table[(n^10 - 30 n^8 + 90 n^7 - 27 n^6 - 270 n^5 + 500 n^4 - 360 n^3 + 96 n^2)/120, {n, 25}] (* or *)
%t A279439 Rest@ CoefficientList[Series[9 x^3*(5 + 201 x + 1239 x^2 + 1755 x^3 + 335 x^4 - 165 x^5 - 11 x^6 + x^7)/(1 - x)^11, {x, 0, 25}], x] (* _Michael De Vlieger_, Dec 22 2016 *)
%o A279439 (PARI) concat(vector(2), Vec(9*x^3*(5 +201*x +1239*x^2 +1755*x^3 +335*x^4 -165*x^5 -11*x^6 +x^7) / (1 -x)^11 + O(x^30))) \\ _Colin Barker_, Dec 22 2016
%Y A279439 Cf. A194190, A279449, A279444, A279445, A197458.
%Y A279439 Same problem but 2,3,4,6..9 points: A083374, A279437, A279438, A279440, A279441, A279442, A279443.
%K A279439 nonn,easy
%O A279439 1,3
%A A279439 _Heinrich Ludwig_, Dec 21 2016