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%I #17 Mar 22 2018 17:32:42
%S 2,-1,2,8,17,29,44,62,83,107,134,164,197,233,272,314,359,407,458,512,
%T 569,629,692,758,827,899,974,1052,1133,1217,1304,1394,1487,1583,1682,
%U 1784,1889,1997,2108,2222,2339,2459,2582,2708,2837,2969,3104,3242,3383,3527,3674
%N a(1)=2; for n>1, a(n) = (4-9*n+3*n^2)/2.
%C Old Name was: A sequence based on odd numbers of the type 3*n + 2: a(n) = a(n - 1) + n - 1; A000096; f(n) = 3*a(n)+2.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F From _Colin Barker_, Apr 14 2014: (Start)
%F a(n) = (4-9*n+3*n^2)/2 for n>1.
%F a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>4.
%F G.f.: x*(3*x^3-11*x^2+7*x-2) / (x-1)^3. (End).
%F a(n) = (n-2)*A095794(n) - (n-1)*A095794(n-1) for n>1. [_Bruno Berselli_, May 19 2015]
%e G.f. = 2*x - x^2 + 2*x^3 + 8*x^4 + 17*x^5 + 29*x^6 + 44*x^7 + 62*x^8 + ...
%t a[0] = 0; a[1] = -1; a[n_] := a[n] = a[n - 1] + n - 1; a1 = Table[a[n], {n, 0, 30}]; f[n_] := 3*a[n] + 2; Table[f[n], {n, 0, 50}]
%t LinearRecurrence[{3,-3,1},{2,-1,2,8},60] (* _Harvey P. Dale_, Mar 22 2018 *)
%o (PARI) Vec(x*(3*x^3-11*x^2+7*x-2)/(x-1)^3 + O(x^100)) \\ _Colin Barker_, Apr 14 2014
%Y Cf. A095794.
%K sign,easy
%O 1,1
%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 20 2008
%E Better name and edits by _Colin Barker_ and _Joerg Arndt_, Apr 14 2014
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