A011898 - OEIS

%I #26 Oct 17 2024 08:25:43

%S 0,0,0,0,1,3,7,13,21,31,45,61,82,107,136,170,210,255,306,363,427,498,

%T 577,664,759,862,975,1096,1228,1370,1522,1685,1860,2046,2244,2454,

%U 2677,2913,3163,3427,3705,3997,4305

%N a(n) = floor(n*(n-1)*(n-2)/16).

%H Vincenzo Librandi, <a href="/A011898/b011898.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,1,-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-16) - 3*a(n-17) + 3*a(n-18) - a(n-19).

%F G.f.: x^4*(1+x^2+2*x^6-2*x^7+3*x^8-x^9+x^11+x^12-x^13+x^14) / ( (1-x)^4*(1+x)*(1+x^2)*(1+x^4)*(1+x^8) ). (End)

%t Table[Floor[(n(n-1)(n-2))/16],{n,0,50}] (* _Harvey P. Dale_, May 16 2012 *)

%o (Magma) [Floor(n*(n-1)*(n-2)/16): n in [0..50]]; // _Vincenzo Librandi_, May 21 2012

%o (PARI) a(n) = n*(n-1)*(n-2)\16; \\ _Michel Marcus_, Jan 14 2018

%o (SageMath) [3*binomial(n,3)//8 for n in range(51)] # _G. C. Greubel_, Oct 16 2024

%Y Cf. A011886.

%K nonn,easy

%O 0,6

%A _N. J. A. Sloane_