

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.


5



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
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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) / ((x1)^9*(x+1)^2).  Colin Barker, Apr 05 2014


MATHEMATICA

Table[(n^8+4*n^714*n^656*n^5+61*n^4+220*n^384*n^2240*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)/((x1)^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



