A240441 Number of ways to place 4 points on a triangular grid of side n so that no three of these points are vertices of an equilateral triangle of any orientation.

0, 0, 3, 114, 969, 4773, 17415, 52125, 135375, 315675, 676200, 1352085, 2553558, 4595934, 7937874, 13229118, 21369330, 33579450, 51487425, 77229900, 113571975, 164046795, 233117313, 326362179, 450688329, 614572413, 828333870, 1104441975, 1457859900, 1906428300

Offset

1,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (7,-19,21,6,-42,42,-6,-21,19,-7,1).

Formula

a(n) = (n^8 + 4*n^7 - 14*n^6 - 56*n^5 + 61*n^4 + 220*n^3 - 84*n^2 - 240*n)/384 + IF(MOD(n, 2) = 1)*(6*n + 3)/32.

G.f.: -3*x^3*(x^4+31*x^3+76*x^2+31*x+1) / ((x-1)^9*(x+1)^2). - Colin Barker, Apr 05 2014

Mathematica

Table[(n^8+4*n^7-14*n^6-56*n^5+61*n^4+220*n^3-84*n^2-240*n)/384 +If[EvenQ[n], 0, (6*n+3)/32], {n, 1, 20}] (* Vaclav Kotesovec, Apr 05 2014 after Heinrich Ludwig *)

Prog

(PARI) concat([0, 0], Vec(-3*x^3*(x^4+31*x^3+76*x^2+31*x+1)/((x-1)^9*(x+1)^2) + O(x^100))) \\ Colin Barker, Apr 05 2014

Crossrefs

Cf. A240439, A240440, A240442.

Sequence in context: A065117 A227794 A225334 * A229929 A267897 A132304

Adjacent sequences: A240438 A240439 A240440 * A240442 A240443 A240444

Keyword

nonn,easy

Author

Heinrich Ludwig, Apr 05 2014

Status

approved