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First differences give (essentially) A028242.
4

%I #22 Sep 24 2022 05:48:09

%S 1,4,9,13,19,24,31,37,45,52,61,69,79,88,99,109,121,132,145,157,171,

%T 184,199,213,229,244,261,277,295,312,331,349,369,388,409,429,451,472,

%U 495,517,541,564,589,613,639,664,691,717,745,772,801,829,859,888,919

%N First differences give (essentially) A028242.

%H Vincenzo Librandi, <a href="/A035104/b035104.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).

%F From _Colin Barker_, Mar 04 2013: (Start)

%F a(n) = (5+3*(-1)^n+28*n+2*n^2)/8.

%F a(n) = 2*a(n-1)-2*a(n-3)+a(n-4).

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

%F Sum_{n>=0} 1/a(n) = 983/990 + tan(3*sqrt(5)*Pi/2)*Pi/(3*sqrt(5)) - cot(2*sqrt(3)*Pi)*Pi/(4*sqrt(3)). - _Amiram Eldar_, Sep 24 2022

%t CoefficientList[Series[(3 x^3 - x^2 - 2 x - 1)/((x - 1)^3 (x + 1)), {x, 0, 60}], x] (* _Vincenzo Librandi_, Oct 20 2013 *)

%o (Magma) [(5+3*(-1)^n+28*n+2*n^2)/8: n in [0..60]]; // _Vincenzo Librandi_, Oct 20 2013

%Y Cf. A004652, A035106, A035107.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Oct 20 2013