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%I #20 Oct 21 2022 20:58:29
%S 0,0,0,0,1,3,6,11,17,26,37,52,69,90,114,143,176,214,257,306,360,420,
%T 486,559,639,726,821,923,1034,1153,1282,1419,1566,1722,1889,2066,2254,
%U 2453,2664,2886,3120,3366,3625,3897,4182,4481,4793,5120,5461,5818,6189
%N [ n(n-1)(n-2)/19 ].
%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-3,3,-1).
%F a(n) = +3*a(n-1) -3*a(n-2) +a(n-3) +a(n-19) -3*a(n-20) +3*a(n-21) -a(n-22). - _R. J. Mathar_, Apr 15 2010
%F G.f.: (x^4 (1+x^4) (1+x^3 (1-x+x^3+x^6) (1+(-1+x) x (1+x^2))))/(1+x (-3+x (3+x (-1+(-1+x)^3 x^16)))). - _Peter J. C. Moses_, Jun 02 2014
%t Table[Floor[n(n-1)(n-2)/19],{n,0,50}] (* or *) LinearRecurrence[{3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-3,3,-1},{0,0,0,0,1,3,6,11,17,26,37,52,69,90,114,143,176,214,257,306,360,420},50] (* _Harvey P. Dale_, May 30 2021 *)
%o (PARI) a(n)=n*(n-1)*(n-2)\19 \\ _Charles R Greathouse IV_, Oct 21 2022
%K nonn,easy
%O 0,6
%A _N. J. A. Sloane_.
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