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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.
4
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
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
KEYWORD
nonn,easy
AUTHOR
Heinrich Ludwig, May 30 2014
STATUS
approved