The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A279450

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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.
(history; published version)

#12 by Ray Chandler at Mon Dec 19 18:38:25 EST 2016

STATUS

proposed

approved

#11 by Colin Barker at Sun Dec 18 08:05:18 EST 2016

STATUS

editing

proposed

#10 by Colin Barker at Sun Dec 18 08:04:55 EST 2016

FORMULA

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

STATUS

reviewed

editing

#9 by Joerg Arndt at Sun Dec 18 07:44:44 EST 2016

STATUS

proposed

reviewed

#8 by Joerg Arndt at Sun Dec 18 07:44:41 EST 2016

STATUS

editing

proposed

#7 by Joerg Arndt at Sun Dec 18 07:44:37 EST 2016

CROSSREFS

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

STATUS

reviewed

editing

#6 by Joerg Arndt at Sun Dec 18 07:44:07 EST 2016

STATUS

proposed

reviewed

#5 by Heinrich Ludwig at Sun Dec 18 06:02:23 EST 2016

STATUS

editing

proposed

#4 by Heinrich Ludwig at Sun Dec 18 05:59:06 EST 2016

LINKS

<a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (6,-8,-22,69,-8,-176,168,182,-364,0,364,-182,-168,176,8,-69,22,8,-6,1).

FORMULA

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).

CROSSREFS

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

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

#3 by Heinrich Ludwig at Sun Dec 18 05:48:25 EST 2016

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.

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.