

A279438


Number of ways to place 4 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.


9



0, 1, 90, 1428, 10600, 51525, 190806, 584080, 1552608, 3701025, 8088850, 16470036, 31616520, 57743413, 101055150, 170433600, 278290816, 441610785, 683206218, 1033218100, 1530887400, 2226630021, 3184447750, 4484709648, 6227340000, 8535450625, 11559457026, 15481719540
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OFFSET

1,3


COMMENTS

Column 5 of triangle A279445.
Rotations and reflections of placements are counted. For numbers if they are to be ignored see A279448.
For condition "no more than 2 points on straight lines at any angle", see A175383.


LINKS

Heinrich Ludwig, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (9,36,84,126,126,84,36,9,1).


FORMULA

a(n) = (n^8  14*n^6 + 30*n^5  17*n^4  6*n^3 + 6*n^2)/24.
a(n) = 9*a(n1)  36*a(n2) + 84*a(n3)  126*a(n4) + 126*a(n5)  84*a(n6) + 36*a(n7)  9*a(n8) + a(n9).
G.f.: x^2*(1 + 81*x + 654*x^2 + 904*x^3 + 99*x^4  57*x^5  2*x^6) / (1  x)^9.  Colin Barker, Dec 13 2016


MATHEMATICA

Table[(n^8  14 n^6 + 30 n^5  17 n^4  6 n^3 + 6 n^2)/24, {n, 28}] (* Michael De Vlieger, Dec 12 2016 *)


PROG

(PARI) concat(0, Vec(x^2*(1 + 81*x + 654*x^2 + 904*x^3 + 99*x^4  57*x^5  2*x^6) / (1  x)^9 + O(x^30))) \\ Colin Barker, Dec 13 2016
(PARI) a(n) = (n^6  14*n^4 + 30*n^3  17*n^2  6*n + 6)*n^2/24 \\ Charles R Greathouse IV, Dec 13 2016


CROSSREFS

Cf. A175383, A249448, A279444, A279445, A197458.
Same problem but 2,3,5..9 points: A083374, A279437, A279439, A279440, A279441, A279442, A279443.
Sequence in context: A155016 A179800 A133350 * A250869 A234983 A166817
Adjacent sequences: A279435 A279436 A279437 * A279439 A279440 A279441


KEYWORD

nonn,easy


AUTHOR

Heinrich Ludwig, Dec 12 2016


STATUS

approved



