A011896 - OEIS

%I #19 Oct 17 2024 15:48:22

%S 0,0,0,0,1,4,8,15,24,36,51,70,94,122,156,195,240,291,349,415,488,570,

%T 660,759,867,985,1114,1253,1404,1566,1740,1926,2125,2338,2564,2805,

%U 3060,3330,3615,3916,4234,4568,4920,5289,5676,6081,6505,6949,7412,7896

%N a(n) = floor( n*(n-1)*(n-2)/14 ).

%H G. C. Greubel, <a href="/A011896/b011896.txt">Table of n, a(n) for n = 0..2000</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 G.f.: x^4*(1+x-x^2+2*x^3-x^4+x^5)/((1-x)^3*(1-x^7)).

%F a(2-n) = (-1)*A055610(n).

%t Table[Floor[(n(n-1)(n-2))/14],{n,0,50}] (* or  *)

%t LinearRecurrence[{3,-3,1,0,0,0,1,-3,3,-1},{0,0,0,0,1,4,8,15,24,36},50] (* _Harvey P. Dale_, Jan 03 2024 *)

%o (PARI) a(n)=n*(n-1)*(n-2)\14

%o (Magma) [Floor(3*Binomial(n,3)/7): n in [0..50]]; // _G. C. Greubel_, Oct 16 2024

%o (SageMath) [3*binomial(n,3)//7 for n in range(51)] # _G. C. Greubel_, Oct 16 2024

%Y Cf. A011886, A055610.

%K nonn

%O 0,6

%A _N. J. A. Sloane_

%E Additional comments from _Michael Somos_, Jun 02 2000.