|
%I #23 Sep 08 2022 08:45:40
%S -2,4,26,76,166,308,514,796,1166,1636,2218,2924,3766,4756,5906,7228,
%T 8734,10436,12346,14476,16838,19444,22306,25436,28846,32548,36554,
%U 40876,45526,50516,55858
%N a(n) = 2*(n^3 + n^2 + n - 1).
%H Vincenzo Librandi, <a href="/A155120/b155120.txt">Table of n, a(n) for n = 0..2000</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) = 2*(n^3 +n^2 +n -1).
%F G.f.: 2*(-1 +6*x -x^2 +2*x^3)/(1-x)^4.
%F E.g.f.: 2*(-1 + 3*x + 4*x^2 + x^3)*exp(x). - _G. C. Greubel_, Mar 25 2021
%p seq( 2*(n^3 +n^2 +n -1), n=0..40); # _G. C. Greubel_, Mar 25 2021
%t Table[-2 +2n +2n^2 +2n^3, {n, 0, 30}]
%t LinearRecurrence[{4,-6,4,-1},{-2,4,26,76},40] (* _Harvey P. Dale_, Jun 06 2014 *)
%o (Magma) [2*(n^3+n^2+n-1): n in [0..40] ]; // _Vincenzo Librandi_, May 23 2011
%o (Sage) [2*(n^3 +n^2 +n -1) for n in (0..40)] # _G. C. Greubel_, Mar 25 2021
%Y Cf. A142463, A155121, A155122, A155123, A155124.
%K sign,easy
%O 0,1
%A _Roger L. Bagula_, Jan 20 2009
|
