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%I #21 Jan 02 2024 09:36:06
%S 0,2,19,39,61,86,114,145,179,216,256,299,345,394,446,501,559,620,684,
%T 751,821,894,970,1049,1131,1216,1304,1395,1489,1586,1686,1789,1895,
%U 2004,2116,2231,2349,2470,2594,2721,2851,2984,3120,3259,3401,3546
%N First differences of A075681.
%H G. C. Greubel, <a href="/A075682/b075682.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = (1/2)*(3*n^2 + 17*n - 38), for n > 3. - _Ralf Stephan_
%F From _G. C. Greubel_, Jan 01 2024: (Start)
%F G.f.: x^2*(2 + 13*x - 12*x^2 + x^3 - x^4)/(1-x)^3.
%F E.g.f.: (1/2)*(-38 + 20*x + 3*x^2)*exp(x) + 19 + 9*x - x^2 - x^3/3!. (End)
%t Join[{0,2,19},LinearRecurrence[{3,-3,1},{39,61,86},50]] (* _Harvey P. Dale_, Aug 26 2014 *)
%o (Magma) [0,2,19] cat [n*(3*n+17)/2 -19: n in [4..50]]; // _G. C. Greubel_, Jan 01 2023
%o (SageMath) [0,2,19]+[n*(3*n+17)/2 -19 for n in range(4,51)] # _G. C. Greubel_, Jan 01 2024
%Y Cf. A075681, A075683.
%K nonn
%O 1,2
%A _Jon Perry_, Oct 12 2002
%E More terms from _Ralf Stephan_