%I #37 Oct 05 2022 19:02:47
%S 3,11,11,19,19,27,27,35,35,43,43,51,51,59,59,67,67,75,75,83,83,91,91,
%T 99,99,107,107,115,115,123,123,131,131,139,139,147,147,155,155,163,
%U 163,171,171,179,179,187,187,195,195,203,203,211,211,219,219,227,227,235,235
%N a(n) = 3 + 8*floor(n/2).
%C More generally, the sequences generated by the recursive relation b(n) = h*n - b(n-1) + k, with b(1)=c and h, k, c, prefixed integers, have the closed form b(n) = (2*h*n + (3*h + 2*k - 4*c)*(-1)^n + h + 2*k)/4. Also, if 2*c = h+k, then b(n) = c + h*floor(n/2); if 2*c = 2*h+k, then b(n) = c + h*floor((n-1)/2); if 2*c = k, b(n) = c + h*floor((n+1)/2). - _Bruno Berselli_, Sep 18 2013
%H Vincenzo Librandi, <a href="/A168378/b168378.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 (1,1,-1).
%F a(n) = 8*n - a(n-1) - 2, with n>1, a(1)=3.
%F G.f.: x*(3 + 8*x - 3*x^2)/((1+x)*(x-1)^2). - _Vincenzo Librandi_, Sep 18 2013
%F a(n) = a(n-1) +a(n-2) -a(n-3). - _Vincenzo Librandi_, Sep 18 2013
%F a(n) = 4*n + 2*(-1)^n + 1. - _Bruno Berselli_, Sep 18 2013
%F a(n) = A168381(n) + 1 = A168398(n) - 1. - _Bruno Berselli_, Sep 18 2013
%F E.g.f.: (4*x + 3)*cosh(x) + (4*x - 1)*sinh(x) - 3. - _G. C. Greubel_, Jul 19 2016
%t Table[ 3 + 8*floor(n/2), {n,60}] (* _Bruno Berselli_, Sep 18 2013 *)
%t CoefficientList[Series[(3 + 8 x - 3 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 18 2013 *)
%t LinearRecurrence[{1,1,-1},{3,11,11},80] (* _Harvey P. Dale_, Oct 05 2022 *)
%o (Magma) [3+8*Floor(n/2): n in [1..70]]; // _Vincenzo Librandi_, Sep 18 2013
%Y Cf. A017101, A168381, A168398.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Nov 24 2009
%E New definition by _Vincenzo Librandi_, Sep 18 2013