A155121 - OEIS

%I #26 Sep 08 2022 08:45:40

%S -3,5,57,237,677,1557,3105,5597,9357,14757,22217,32205,45237,61877,

%T 82737,108477,139805,177477,222297,275117,336837,408405,490817,585117,

%U 692397,813797,950505,1103757,1274837,1465077,1675857

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

%H Vincenzo Librandi, <a href="/A155121/b155121.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

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

%F G.f.: (3 - 20*x - 2*x^2 - 32*x^3 + 3*x^4)/(x-1)^5.

%F From _Bruno Berselli_, Dec 16 2010: (Start)

%F a(n) = 4*A071237(n) - 3.

%F a(n) = 2*A024003(n)/(1-n) - 5 (n>1). (End)

%F E.g.f.: (-3 + 8*x + 22*x^2 + 14*x^3 + 2*x^4)*exp(x). - _G. C. Greubel_, Mar 25 2021

%p seq( -3 +2*n +2*n^2 +2*n^3 +2*n^4, n=0..40); # _G. C. Greubel_, Mar 25 2021

%t Table[-3 +2n +2n^2 +2n^3 +2n^4, {n, 0, 30}]

%o (Magma) [2*n*(1+n+n^2+n^3)-3: n in [0..40] ]; // _Vincenzo Librandi_, May 23 2011

%o (Sage) [-3 +2*n +2*n^2 +2*n^3 +2*n^4 for n in (0..40)] # _G. C. Greubel_, Mar 25 2021

%Y Cf. A024003, A071237, A142463, A155120.

%K sign,easy

%O 0,1

%A _Roger L. Bagula_, Jan 20 2009