A279448 - OEIS

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.

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