A011909 - OEIS

%I #24 Oct 19 2024 21:27:32

%S 0,0,0,0,0,2,4,7,12,18,26,36,48,63,80,101,124,151,181,215,253,295,342,

%T 393,449,511,577,650,728,812,902,998,1102,1212,1329,1454,1586,1726,

%U 1874,2030,2195,2368,2551,2742,2943,3153,3373,3603,3843,4094,4355,4627,4911,5205,5512,5830,6160,6502,6856,7224,7604,7997,8404,8824,9258,9706,10168,10645,11136

%N a(n) = floor( n*(n-1)*(n-2)/27 ).

%H G. C. Greubel, <a href="/A011909/b011909.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_28">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,4,-1).

%F G.f.: x^5*(1-x+x^2)*(2-2*x-x^2+3*x^3-2*x^4+3*x^6-3*x^7+2*x^9-x^10-x^11 +3*x^12-2*x^13-x^14+3*x^15-2*x^16+2*x^18-2*x^19+x^20)/((1-x)^4*(1+x^3+x^6)*(1+x^9+x^18)). - _Peter J. C. Moses_, Jun 02 2014

%t Table[Floor[n(n-1)(n-2)/27],{n,0,80}] (* or *)

%t LinearRecurrence[{4,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,4,-1},{0,0,0,0,0,2,4,7,12,18,26,36,48,63,80,101,124,151,181,215,253,295, 342,393,449,511,577,650}, 81] (* _Harvey P. Dale_, Jun 12 2023 *)

%o (Magma) [Floor(2*Binomial(n,3)/9): n in [0..80]]; // _G. C. Greubel_, Oct 19 2024

%o (SageMath) [2*binomial(n,3)//9 for n in range(81)] # _G. C. Greubel_, Oct 19 2024

%Y Cf. A011886.

%K nonn

%O 0,6

%A _N. J. A. Sloane_

%E More terms added by _G. C. Greubel_, Oct 19 2024