A243143 Number of inequivalent (mod D_3) ways to place 4 points on a triangular grid of side n so that they are not vertices of an equilateral triangle of any orientation.

1, 22, 170, 816, 2947, 8765, 22703, 52823, 113042, 225817, 426299, 766905, 1324282, 2206478, 3563770, 5599258, 8584775, 12875840, 18934040, 27347390, 38860741, 54402707, 75125825, 102441321, 138070912, 184090795, 242997153, 317760863, 411908932, 529591532, 675681764

Offset

3,2

Links

Heinrich Ludwig, Table of n, a(n) for n = 3..1000

Index entries for linear recurrences with constant coefficients, signature (5,-7,-5,23,-19,-7,27,-27,7,19,-23,5,7,-5,1).

Formula

a(n) = (n^8 + 4*n^7 - 14*n^6 - 56*n^5 + 136*n^4 - 104*n^3 + 552*n^2 - 672*n)/2304 + IF(MOD(n, 2) = 1)*(28*n^3 - 198*n^2 + 296*n + 21)/768) + IF(MOD(n-1, 4) <= 1)*(-1/8).

G.f.: -x^3*(3*x^10 -10*x^9 +19*x^8 -13*x^7 +102*x^6 +105*x^5 +144*x^4 +125*x^3 +67*x^2 +17*x +1) / ((x -1)^9*(x +1)^4*(x^2 +1)). - Colin Barker, May 30 2014

Mathematica

Drop[CoefficientList[Series[-x^3*(3*x^10 - 10*x^9 + 19*x^8 - 13*x^7 + 102*x^6 + 105*x^5 + 144*x^4 + 125*x^3 + 67*x^2 + 17*x + 1) / ((x-1)^9*(x+1)^4*(x^2+1)), {x, 0, 40}], x], 3] (* Vaclav Kotesovec, May 31 2014 after Colin Barker *)

Crossrefs

Cf. A243141, A240441, A001399, A227327, A243142, A243144.

Sequence in context: A224156 A223775 A224407 * A321268 A086604 A041932

Adjacent sequences: A243140 A243141 A243142 * A243144 A243145 A243146

Keyword

nonn,easy

Author

Heinrich Ludwig, May 30 2014

Status

approved