A239570 Number of ways to place 4 points on a triangular grid of side n so that no two of them are adjacent.

0, 1, 114, 1137, 6100, 23265, 71211, 186739, 436437, 932850, 1856305, 3483546, 6224439, 10668112, 17640000, 28271370, 44083006, 67084839, 99893412, 145869175, 209275710, 295463091, 411077689, 564300837, 765118875, 1025627200, 1360371051, 1786725864, 2325320137

Offset

3,3

Comments

Rotations and reflections of placements are counted. If they are to be ignored see A239574.

Links

Vincenzo Librandi, Table of n, a(n) for n = 3..1000

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1)

Formula

a(n) = (n-2)*(n-3)*(n^6+9*n^5-39*n^4-353*n^3+950*n^2+4040*n-11904)/384.

G.f.: x^4*(38*x^6-156*x^5+153*x^4+113*x^3-147*x^2-105*x-1) / (x-1)^9. - Colin Barker, Mar 22 2014

Mathematica

CoefficientList[Series[x (38 x^6 - 156 x^5 + 153 x^4 + 113 x^3 - 147 x^2 - 105 x - 1)/(x - 1)^9, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 23 2014 *)

Prog

(PARI) concat(0, Vec(x^4*(38*x^6-156*x^5+153*x^4+113*x^3-147*x^2-105*x-1)/(x-1)^9 + O(x^100))) \\ Colin Barker, Mar 22 2014
(Magma) [(n^2-5*n+6)*(n^6+9*n^5-39*n^4-353*n^3+950*n^2 +4040*n-11904)/384: n in [3..40]]: // Vincenzo Librandi, Mar 23 2014

Crossrefs

Cf. A239567, A239574, A239568 (2 points), A239569 (3 points), A239571 (5 points), A282998 (6 points).

Sequence in context: A353746 A251459 A251452 * A002952 A296403 A262416

Adjacent sequences: A239567 A239568 A239569 * A239571 A239572 A239573

Keyword

nonn,easy

Author

Heinrich Ludwig, Mar 22 2014

Status

approved