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A011912
a(n) = floor(n*(n-1)*(n-2)/30).
2
0, 0, 0, 0, 0, 2, 4, 7, 11, 16, 24, 33, 44, 57, 72, 91, 112, 136, 163, 193, 228, 266, 308, 354, 404, 460, 520, 585, 655, 730, 812, 899, 992, 1091, 1196, 1309, 1428, 1554, 1687, 1827, 1976, 2132, 2296, 2468, 2648, 2838, 3036, 3243, 3459, 3684, 3920, 4165, 4420, 4685, 4960, 5247, 5544, 5852, 6171, 6501, 6844, 7198, 7564, 7942, 8332, 8736, 9152, 9581, 10023, 10478, 10948
OFFSET
0,6
FORMULA
From R. J. Mathar, Apr 15 2010: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-5) - 3*a(n-6) + 3*a(n-7) - a(n-8).
G.f.: x^5*(2-2*x+x^2) / ( (1-x)^4*(1+x+x^2+x^3+x^4) ). (End)
MAPLE
seq(floor(binomial(n, 3)/5), n=0..80); # Zerinvary Lajos, Jan 12 2009
MATHEMATICA
Table[Floor[(n(n-1)(n-2))/30], {n, 0, 80}] (* or *) LinearRecurrence[{3, -3, 1, 0, 1, -3, 3, -1}, {0, 0, 0, 0, 0, 2, 4, 7}, 81] (* Harvey P. Dale, Jun 20 2011 *)
CoefficientList[Series[x^5*(x^2-2*x+2)/((-1+x)^4*(x^4+x^3+x^2+x+1)), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 07 2012 *)
PROG
(Magma) [Floor(n*(n-1)*(n-2)/30): n in [0..80]]; // Vincenzo Librandi, Jul 07 2012
(SageMath) [binomial(n, 3)//5 for n in range(81)] # G. C. Greubel, Oct 19 2024
CROSSREFS
Cf. A011886.
Sequence in context: A320591 A129339 A196719 * A063676 A099385 A331387
KEYWORD
nonn,easy
STATUS
approved