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A279448 Number of nonequivalent 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. 6
0, 1, 17, 202, 1397, 6582, 24185, 73496, 195086, 463875, 1013505, 2061426, 3956947, 7222992, 12640817, 21312992, 34801420, 55215621, 85424721, 129174250, 191397185, 278361226, 398108777, 560635032, 778491962, 1066995527, 1445034305, 1935301746, 2565356031, 3367870500 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Column 5 of A279453.

Rotations and reflections of placements are not counted. For numbers if they are to be counted see A279438.

For condition "no more than 2 points on straight lines at any angle", see A235455.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (4,-1,-16,19,20,-45,0,45,-20,-19,16,1,-4,1).

FORMULA

a(n) = (n^8 - 14*n^6 + 30*n^5 + 12*n^4 - 60*n^3 + 40*n^2)/192 + IF(MOD(n, 2) = 1, 4*n^4 - 20*n^3 + 22*n^2 - 2*n - 7)/64.

a(n) = 4*a(n-1) - a(n-2) - 16*a(n-3) + 19*a(n-4) + 20*a(n-5) - 45*a(n-6) + 45*a(n-8) - 20*a(n-9) - 19*a(n-10) + 16*a(n-11) + a(n-12) - 4*a(n-13) + a(n-14).

G.f.: x^2*(1 +13*x +135*x^2 +622*x^3 +1449*x^4 +2143*x^5 +1557*x^6 +781*x^7 +34*x^8 -8*x^9 -8*x^10 +x^11) / ((1 -x)^9*(1 +x)^5). - Colin Barker, Dec 18 2016

PROG

(PARI) concat(0, Vec(x^2*(1 +13*x +135*x^2 +622*x^3 +1449*x^4 +2143*x^5 +1557*x^6 +781*x^7 +34*x^8 -8*x^9 -8*x^10 +x^11) / ((1 -x)^9*(1 +x)^5) + O(x^40))) \\ Colin Barker, Dec 18 2016

CROSSREFS

Cf. A235455, A279438, A279452, A279453, A279454.

Same problem but 2,3,5,6,7 points: A014409, A279447, A279449, A279450, A279451.

Sequence in context: A021134 A065895 A009479 * A017897 A016311 A140961

Adjacent sequences:  A279445 A279446 A279447 * A279449 A279450 A279451

KEYWORD

nonn,easy

AUTHOR

Heinrich Ludwig, Dec 18 2016

STATUS

approved

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Last modified April 11 03:50 EDT 2021. Contains 342886 sequences. (Running on oeis4.)