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A155120 a(n) = 2*(n^3 + n^2 + n - 1). 3

%I

%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

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Last modified April 16 12:45 EDT 2021. Contains 343037 sequences. (Running on oeis4.)