A011902 - OEIS

%I #22 Oct 18 2024 06:08:35

%S 0,0,0,0,1,3,6,10,16,25,36,49,66,85,109,136,168,204,244,290,342,399,

%T 462,531,607,690,780,877,982,1096,1218,1348,1488,1636,1795,1963,2142,

%U 2331,2530,2741,2964,3198,3444,3702,3973,4257,4554,4864,5188,5527,5880,6247,6630,7027,7441,7870,8316,8778,9256,9752,10266,10797,11346,11913,12499,13104,13728,14371

%N a(n) = floor( n*(n-1)*(n-2)/20 ).

%H G. C. Greubel, <a href="/A011902/b011902.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-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-20) -3*a(n-21) +3*a(n-22) -a(n-23).

%F G.f.: x^4*(1+x^4+x^5-x^6+2*x^8-2*x^9+3*x^10-2*x^11+2*x^12-x^13+2*x^15-x^17+x^18)/((1-x)^4*(1+x)*(1+x^2)*(1+x+x^2+x^3+x^4)*(1-x+x^2-x^3+x^4)*(1-x^2+x^4-x^6+x^8)). (End)

%t Table[Floor[(n(n-1)(n-2))/20],{n,0,80}]  (* _Harvey P. Dale_, Mar 23 2011 *)

%o (Magma) [Floor(3*Binomial(n,3)/10): n in [0..80]]; // _G. C. Greubel_, Oct 18 2024

%o (SageMath) [3*binomial(n,3)//10 for n in range(81)] # _G. C. Greubel_, Oct 18 2024

%Y Cf. A011886.

%K nonn,easy

%O 0,6

%A _N. J. A. Sloane_

%E More terms added by _G. C. Greubel_, Oct 18 2024