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A279449 Number of nonequivalent 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. 6
0, 0, 9, 306, 4361, 34059, 185181, 777280, 2710074, 8181558, 22067973, 54285858, 123791067, 264749849, 536146569, 1035584592, 1919530804, 3430908108, 5937810417, 9984193986, 16358592141, 26181281511, 41019234245, 63028246512, 95136210222, 141264963970, 206611069197 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Column 6 of A279453.

Rotations and reflections of placements are not counted. For numbers if they are to be counted see A279439.

For condition "no more than 2 points on straight lines at any angle", see A235456.

LINKS

Heinrich Ludwig, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,-4,-20,40,16,-100,44,110,-110,-44,100,-16,-40,20,4,-5,1).

FORMULA

a(n) = (n^10 - 30*n^8 + 90*n^7 - 27*n^6 - 218*n^5 + 340*n^4 - 340*n^3 + 376*n^2 - 192*n)/960 + IF(MOD(n, 2) = 1, 2*n^5 - 9*n^4 + 14*n^3 - 6*n^2 - 4*n + 3)/64.

a(n) = 5*a(n-1) - 4*a(n-2) - 20*a(n-3) + 40*a(n-4) + 16*a(n-5) - 100*a(n-6) + 44*a(n-7) + 110*a(n-8) - 110*a(n-9) - 44*a(n-10) + 100*a(n-11) - 16*a(n-12) - 40*a(n-13) + 20*a(n-14) + 4*a(n-15) - 5*a(n-16) + a(n-17).

G.f.: x^3*(9 +261*x +2867*x^2 +13658*x^3 +38090*x^4 +62447*x^5 +67142*x^6 +41996*x^7 +15541*x^8 +955*x^9 -761*x^10 -278*x^11 -8*x^12 +x^13) / ((1 -x)^11*(1 +x)^6). - Colin Barker, Dec 18 2016

PROG

(PARI) concat(vector(2), Vec(x^3*(9 +261*x +2867*x^2 +13658*x^3 +38090*x^4 +62447*x^5 +67142*x^6 +41996*x^7 +15541*x^8 +955*x^9 -761*x^10 -278*x^11 -8*x^12 +x^13) / ((1 -x)^11*(1 +x)^6) + O(x^40))) \\ Colin Barker, Dec 18 2016

CROSSREFS

Cf. A235456, A279439, A279452, A279453, A279454.

Same problem but 2,3,4,6,7 points: A014409, A279447, A279448, A279450, A279451.

Sequence in context: A196694 A196727 A197067 * A152437 A296802 A231133

Adjacent sequences:  A279446 A279447 A279448 * A279450 A279451 A279452

KEYWORD

nonn,easy

AUTHOR

Heinrich Ludwig, Dec 18 2016

STATUS

approved

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Last modified May 27 04:33 EDT 2020. Contains 334649 sequences. (Running on oeis4.)