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A239570 Number of ways to place 4 points on a triangular grid of side n so that no two of them are adjacent. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A174072 A251459 A251452 * A002952 A296403 A262416

Adjacent sequences:  A239567 A239568 A239569 * A239571 A239572 A239573

KEYWORD

nonn,easy

AUTHOR

Heinrich Ludwig, Mar 22 2014

STATUS

approved

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Last modified November 16 17:25 EST 2019. Contains 329201 sequences. (Running on oeis4.)