A172193 - OEIS

%I #21 Apr 28 2022 07:47:17

%S 1,37,83,139,205,281,367,463,569,685,811,947,1093,1249,1415,1591,1777,

%T 1973,2179,2395,2621,2857,3103,3359,3625,3901,4187,4483,4789,5105,

%U 5431,5767,6113,6469,6835,7211,7597,7993,8399,8815,9241,9677,10123,10579

%N a(n) = 5*n^2 + 31*n + 1.

%H Vincenzo Librandi, <a href="/A172193/b172193.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.: (1+34*x-25*x^2)/(1-x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Apr 07 2013

%F E.g.f.: (1 + 36*x + 5*x^2)*exp(x). - _G. C. Greubel_, Apr 28 2022

%t CoefficientList[Series[(1 +34x -25x^2)/(1-x)^3, {x, 0, 60}], x] (* _Vincenzo Librandi_, Apr 07 2013 *)

%o (Magma) [ 5*n^2+31*n+1: n in [0..50] ];

%o (PARI) a(n)=5*n^2+31*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017

%o (SageMath) [((10*n+31)^2 -941)/20 for n in (0..50)] # _G. C. Greubel_, Apr 28 2022

%Y Cf. A172043 (5*n^2-n+1).

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Jan 29 2010

%E Replaced definition with formula. - _N. J. A. Sloane_, Mar 03 2010