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A168233 a(n) = 3*n - a(n-1) - 1 for n>0, a(1)=1.

%I A168233 #31 Sep 08 2022 08:45:48
%S A168233 1,4,4,7,7,10,10,13,13,16,16,19,19,22,22,25,25,28,28,31,31,34,34,37,
%T A168233 37,40,40,43,43,46,46,49,49,52,52,55,55,58,58,61,61,64,64,67,67,70,70,
%U A168233 73,73,76,76,79,79,82,82,85,85,88,88,91,91,94,94,97,97,100,100,103,103,106
%N A168233 a(n) = 3*n - a(n-1) - 1 for n>0, a(1)=1.
%H A168233 Vincenzo Librandi, <a href="/A168233/b168233.txt">Table of n, a(n) for n = 1..1000</a>
%H A168233 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A168233 From _Bruno Berselli_, Nov 15 2010: (Start)
%F A168233 a(n) = (6*n + 3*(-1)^n + 1)/4.
%F A168233 G.f.: x*(1 + 3*x - x^2)/((1+x)*(1-x)^2).
%F A168233 a(n) = a(n-1) + a(n-2) - a(n-3), for n>3.
%F A168233 a(n) + a(n-1) = A016789(n-1) for n>1.
%F A168233 a(n) - a(n-1-2*k) = A010674(n-1) + A008585(k) for n>2*k+1 and k in A001477.
%F A168233 a(n) - a(n-2*k) = A008585(k) for n>2*k and k in A001477. (End)
%F A168233 a(n+1) = A016777(floor((n+1)/2)). - _R. J. Mathar_, Jan 03 2011
%F A168233 E.g.f.: (1/4)*(3 - 4*exp(x) + (1 + 6*x)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 16 2016
%p A168233 a:=n->3*floor(n/2)+1; seq(a(k), k = 1..70); # _Wesley Ivan Hurt_, Feb 01 2013
%t A168233 CoefficientList[Series[(1 + 3*x - x^2)/((1+x) * (1-x)^2), {x, 0, 100}], x] (* _Vincenzo Librandi_, Feb 02 2013 *)
%t A168233 LinearRecurrence[{1,1,-1},{1,4,4},80] (* _Harvey P. Dale_, Oct 13 2015 *)
%o A168233 (Magma) [(6*n + 3*(-1)^n + 1)/4: n in [1..70]]; // _Vincenzo Librandi_, Feb 02 2013
%Y A168233 Cf. A008585, A001477, A016777, A010674, A016789.
%K A168233 nonn,easy
%O A168233 1,2
%A A168233 _Vincenzo Librandi_, Nov 21 2009