A011889 - OEIS

%I #31 Oct 10 2024 05:22:20

%S 0,0,0,0,3,8,17,30,48,72,102,141,188,245,312,390,480,582,699,830,977,

%T 1140,1320,1518,1734,1971,2228,2507,2808,3132,3480,3852,4251,4676,

%U 5129,5610,6120,6660,7230,7833,8468,9137,9840,10578,11352,12162,13011,13898,14825,15792,16800

%N a(n) = floor(n*(n-1)*(n-2)/7).

%H Vincenzo Librandi, <a href="/A011889/b011889.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,0,0,1,-3,3,-1).

%F From _R. J. Mathar_, Apr 15 2010: (Start)

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-7) - 3*a(n-8) + 3*a(n-9) - a(n-10).

%F G.f.: x^4*(3-x+2*x^2+x^4+x^5) / ( (1-x)^4*(1+x+x^2+x^3+x^4+x^5+x^6) ). (End)

%t CoefficientList[Series[x^4*(3-x+2*x^2+x^4+x^5)/((-1+x)^4*(1+x+x^2+x^3+ x^4+x^5+x^6)),{x,0,50}],x] (* _Vincenzo Librandi_ Jul 07 2012 *)

%t Floor[6*Binomial[Range[0,50], 3]/7] (* _G. C. Greubel_, Oct 06 2024 *)

%o (Magma) [Floor(n*(n-1)*(n-2)/7): n in [0..50]]; // _Vincenzo Librandi_, Jul 07 2012

%o (SageMath) [6*binomial(n,3)//7 for n in range(51)] # _G. C. Greubel_, Oct 06 2024

%Y Cf. A011886.

%K nonn,easy

%O 0,5

%A _N. J. A. Sloane_