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%I #16 Sep 08 2022 08:46:13
%S -8,-7,0,19,56,117,208,335,504,721,992,1323,1720,2189,2736,3367,4088,
%T 4905,5824,6851,7992,9253,10640,12159,13816,15617,17568,19675,21944,
%U 24381,26992,29783,32760,35929,39296,42867,46648,50645,54864,59311,63992
%N a(n) = n^3 - 8.
%C The cubic number sequence whose geometrical arrangement loses all vertices: this is a figurate number represented by a cubic lattice of n^3 equispaced points without vertices.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F G.f.: (-8 + 25*x - 20*x^2 + 9*x^3)/(1-x)^4. - _Vincenzo Librandi_, Jun 25 2015
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, Jun 25 2015
%t Table[n^3 - 8, {n, 0, 40}] (* _Vincenzo Librandi_, Jun 25 2015 *)
%t LinearRecurrence[{4,-6,4,-1},{-8,-7,0,19},50] (* _Harvey P. Dale_, Sep 25 2017 *)
%o (Magma) [n^3 - 8: n in [0..40]]; // _Vincenzo Librandi_, Jun 25 2015
%K sign,easy
%O 0,1
%A _Luciano Ancora_, Jun 24 2015
%E First term -8 added from _Vincenzo Librandi_, Jun 25 2015
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