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%I #25 Sep 08 2022 08:45:29
%S -1,5,23,59,119,209,335,503,719,989,1319,1715,2183,2729,3359,4079,
%T 4895,5813,6839,7979,9239,10625,12143,13799,15599,17549,19655,21923,
%U 24359,26969,29759,32735,35903,39269,42839,46619,50615,54833,59279,63959,68879,74045,79463
%N a(n) = n^3 - n - 1.
%C Given three consecutive numbers x=n-2, y=n-1 and z=n, the sum over all products is x*y*z + x*y + x*z + y*z + x + y + z = n^3 - n - 1 = a(n). - _J. M. Bergot_, Aug 25 2011
%H Vincenzo Librandi, <a href="/A126420/b126420.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F For n > 1, a(n) = floor(n^6/(n^3+n+1)). - _Gary Detlefs_, Feb 10 2010
%F G.f.: x*(-1 + 9*x - 3*x^2 + x^3) / (x-1)^4. - _R. J. Mathar_, Aug 28 2011
%F a(-n) = -A061600(n). - _Bruno Berselli_, Aug 29 2011
%F E.g.f.: (-1 + 6*x + 6*x^2 + x^3)*exp(x) = -E(0) where E(k) = 1 - 6*x/(1 - x/(1 + x - x/(6 + x - 6/(1 - x^2*(k+1)/E(k+1) )))); (recursively defined continued fraction). - _Sergei N. Gladkovskii_, Jan 09 2013
%t a = {}; Do[AppendTo[a, x^3 - x - 1], {x, 1, 100}]; a
%o (Magma) [n^3-n-1: n in [1..50]]; // _Vincenzo Librandi_, Aug 29 2011
%Y Cf. A002327, A116581.
%K sign,easy
%O 1,2
%A _Artur Jasinski_, Dec 26 2006
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