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%I #32 Sep 08 2022 08:44:35
%S 0,4,56,216,544,1100,1944,3136,4736,6804,9400,12584,16416,20956,26264,
%T 32400,39424,47396,56376,66424,77600,89964,103576,118496,134784,
%U 152500,171704,192456,214816,238844,264600,292144,321536,352836,386104,421400,458784,498316,540056
%N a(n) = 10*n^3 - 6*n^2.
%D W. A. Whitworth, DCC Exercises in Choice and Chance, Stechert, NY, 1945, p. 29.
%H Vincenzo Librandi, <a href="/A006592/b006592.txt">Table of n, a(n) for n = 0..10000</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) = 4 * A006597(n).
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=0, a(1)=4, a(2)=56, a(3)=216. - _Harvey P. Dale_, Aug 13 2012
%F From _G. C. Greubel_, Oct 18 2018: (Start)
%F G.f.: 4*(x + 10*x^2 + 4*x^3)/(1 - x)^4.
%F E.g.f.: 2*x*(2 + 12*x + 5*x^2)*exp(x). (End)
%t Table[10n^3-6n^2,{n,0,50}] (* or *) LinearRecurrence[{4,-6,4,-1},{0,4,56,216},50] (* _Harvey P. Dale_, Aug 13 2012 *)
%o (Magma) [10*n^3-6*n^2: n in [0..40]]; // _Vincenzo Librandi_, Jul 20 2011
%o (PARI) a(n)=10*n^3-6*n^2;
%K easy,nonn
%O 0,2
%A _N. J. A. Sloane_
%E Name corrected by _Arkadiusz Wesolowski_, Jul 20 2011
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