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a(n) = floor( n*(n-1)*(n-2)/25 ).
2

%I #18 Oct 18 2024 06:09:22

%S 0,0,0,0,0,2,4,8,13,20,28,39,52,68,87,109,134,163,195,232,273,319,369,

%T 425,485,552,624,702,786,876,974,1078,1190,1309,1436,1570,1713,1864,

%U 2024,2193,2371,2558,2755,2961,3178,3405,3643,3891,4151,4421,4704,4998,5304,5622,5952,6296,6652,7022,7405,7802,8212,8637,9076,9530,9999,10483,10982,11497,12027

%N a(n) = floor( n*(n-1)*(n-2)/25 ).

%H G. C. Greubel, <a href="/A011907/b011907.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 (3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-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-25) -3*a(n-26) +3*a(n-27) -a(n-28).

%F G.f.: x^5*(2-2*x+2*x^2-x^3+x^4-x^5+2*x^6-x^7+x^8+x^12-x^13+2*x^14-x^15+x^16-x^17+2*x^18-2*x^19+3*x^20-2*x^21+x^22) / ( (1-x)^4*(1+x^4+x^3+x^2+x)*(1+x^5+x^10+x^15+x^20) ). (End)

%t Table[Floor[(n(n-1)(n-2))/25],{n,0,75}] (* _Harvey P. Dale_, Aug 25 2021 *)

%o (PARI) a(n)=n*(n-1)*(n-2)\25 \\ _Charles R Greathouse IV_, Oct 21 2022

%o (Magma) [Floor(6*Binomial(n,3)/25): n in [0..75]]; // _G. C. Greubel_, Oct 18 2024

%o (SageMath) [6*binomial(n,3)//25 for n in range(76)] # _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