login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A279450 Number of nonequivalent ways to place 6 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, 2, 285, 9110, 126396, 1055025, 6266614, 29198740, 113262680, 380775248, 1140764611, 3108667306, 7824370092, 18407341855, 40855872764, 86201399496, 173952773328, 337453762782, 631982899545, 1146743732126, 2022212701212, 3474824082125, 5831439251154, 9576836632860 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Column 7 of A279453.

Rotations and reflections of placements are not counted. For numbers if they are to be counted see A279440.

For condition "no more than 2 points on straight lines at any angle", see A235457.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (6,-8,-22,69,-8,-176,168,182,-364,0,364,-182,-168,176,8,-69,22,8,-6,1).

FORMULA

a(n) = (n^12 - 55*n^10 + 210*n^9 + 93*n^8 - 2220*n^7 + 6052*n^6 - 8040*n^5 + 4236*n^4 + 3240*n^3 - 5872*n^2 + 2400*n)/5760 + IF(MOD(n, 2) = 1, 2*n^6 - 18*n^5 + 53*n^4 - 64*n^3 + 33*n^2 - 12*n + 5)/128.

a(n) = 6*a(n-1) - 8*a(n-2) - 22*a(n-3) + 69*a(n-4) - 8*a(n-5) - 176*a(n-6) + 168*a(n-7) + 182*a(n-8) - 364*a(n-9) + 364*a(n-11) - 182*a(n-12) - 168*a(n-13) + 176*a(n-14) + 8*a(n-15) - 69*a(n-16) + 22*a(n-17) + 8*a(n-18) - 6*a(n-19) + *a(n-20).

G.f.: x^3*(2 +273*x +7416*x^2 +74060*x^3 +375661*x^4 +1128403*x^5 +2194010*x^6 +2815082*x^7 +2424155*x^8 +1294751*x^9 +376028*x^10 -5296*x^11 -32173*x^12 -8195*x^13 +178*x^14 +122*x^15 +3*x^16) / ((1 -x)^13*(1 +x)^7). - Colin Barker, Dec 18 2016

PROG

(PARI) concat(vector(2), Vec(x^3*(2 +273*x +7416*x^2 +74060*x^3 +375661*x^4 +1128403*x^5 +2194010*x^6 +2815082*x^7 +2424155*x^8 +1294751*x^9 +376028*x^10 -5296*x^11 -32173*x^12 -8195*x^13 +178*x^14 +122*x^15 +3*x^16) / ((1 -x)^13*(1 +x)^7) + O(x^40))) \\ Colin Barker, Dec 18 2016

CROSSREFS

Cf. A235457, A279440, A279452, A279453, A279454.

Same problem but 2,3,4,5,7 points: A014409, A279447, A279448, A279449, A279451.

Sequence in context: A277879 A307470 A182519 * A163276 A065498 A296591

Adjacent sequences:  A279447 A279448 A279449 * A279451 A279452 A279453

KEYWORD

nonn,easy

AUTHOR

Heinrich Ludwig, Dec 18 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 19 10:41 EDT 2020. Contains 337178 sequences. (Running on oeis4.)