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%I #17 Sep 08 2022 08:45:29
%S -120,-15,48,75,72,45,0,-57,-120,-183,-240,-285,-312,-315,-288,-225,
%T -120,33,240,507,840,1245,1728,2295,2952,3705,4560,5523,6600,7797,
%U 9120,10575,12168,13905,15792,17835,20040,22413,24960,27687,30600,33705,37008,40515,44232,48165
%N Q(n,6), where Q(m,k) is defined in A127080 and A127137.
%D V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.
%H Colin Barker, <a href="/A127148/b127148.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = n^3 -24*n^2 +128*n -120.
%F a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4), a(0)=-120, a(1)=-15, a(2)=48, a(3)=75. - _Harvey P. Dale_, Oct 22 2013
%F G.f.: (-3)*(40-155*x+204*x^2-91*x^3)/(1-x)^4. - _Colin Barker_, Nov 11 2014
%F E.g.f.: (-120 + 105*x - 21*x^2 + x^3)*exp(x). - _G. C. Greubel_, Aug 12 2019
%p seq(n^3 -24*n^2 +128*n -120, n=0..50); # _G. C. Greubel_, Aug 12 2019
%t Table[n^3-24n^2+128n-120,{n,0,50}] (* or *) LinearRecurrence[{4,-6,4,-1},{-120,-15,48,75},50] (* _Harvey P. Dale_, Oct 22 2013 *)
%o (PARI) Vec(3*(91*x^3-204*x^2+155*x-40)/(x-1)^4 + O(x^50)) \\ _Colin Barker_, Nov 11 2014
%o (Magma) [n^3 -24*n^2 +128*n -120: n in [0..50]]; // _G. C. Greubel_, Aug 12 2019
%o (Sage) [n^3 -24*n^2 +128*n -120 for n in (0..50)] # _G. C. Greubel_, Aug 12 2019
%o (GAP) List([0..50], n-> n^3 -24*n^2 +128*n -120); # _G. C. Greubel_, Aug 12 2019
%Y A row of A127080.
%K sign,easy
%O 0,1
%A _N. J. A. Sloane_, Mar 24 2007
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