A243142 Number of inequivalent (mod D_3) ways to place 3 points on a triangular grid of side n so that they are not vertices of an equilateral triangle of any orientation.

0, 3, 19, 75, 218, 542, 1178, 2350, 4340, 7585, 12605, 20153, 31094, 46620, 68068, 97212, 136008, 186975, 252855, 337095, 443410, 576378, 740894, 942890, 1188668, 1485757, 1842113, 2267125, 2770670, 3364280, 4060040, 4871928, 5814544, 6904635, 8159643, 9599427

Offset

2,2

Links

Heinrich Ludwig, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (4,-3,-8,14,0,-14,8,3,-4,1).

Formula

a(n) = (n^6 + 3*n^5 - 5*n^4 + 6*n^3 - 68*n^2 + 72*n + IF(MOD(n, 2) = 1)*(27*n^2 - 81*n + 45))/288.

G.f.: x^3*(2*x^5-5*x^4+x^3-8*x^2-7*x-3) / ((x-1)^7*(x+1)^3). - Colin Barker, May 30 2014

Mathematica

Drop[CoefficientList[Series[x^3*(2*x^5-5*x^4+x^3-8*x^2-7*x-3) / ((x-1)^7*(x+1)^3), {x, 0, 40}], x], 2] (* Vaclav Kotesovec, May 31 2014 after Colin Barker *)

Prog

(PARI) concat(0, Vec(x^3*(2*x^5-5*x^4+x^3-8*x^2-7*x-3)/((x-1)^7*(x+1)^3) + O(x^100))) \\ Colin Barker, May 30 2014

Crossrefs

Cf. A243141, A240440, A001399, A227327, A243143, A243144.

Sequence in context: A202041 A245507 A247059 * A174286 A336589 A240746

Adjacent sequences: A243139 A243140 A243141 * A243143 A243144 A243145

Keyword

nonn,easy

Author

Heinrich Ludwig, May 30 2014

Status

approved