A168337 - OEIS

%I #24 Sep 08 2022 08:45:49

%S 1,8,8,15,15,22,22,29,29,36,36,43,43,50,50,57,57,64,64,71,71,78,78,85,

%T 85,92,92,99,99,106,106,113,113,120,120,127,127,134,134,141,141,148,

%U 148,155,155,162,162,169,169,176,176,183,183,190,190,197,197,204,204,211

%N a(n) = 1 + 7*floor(n/2).

%H Vincenzo Librandi, <a href="/A168337/b168337.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) = 7*n - a(n-1) - 5, with n>1, a(1)=1.

%F From _Vincenzo Librandi_, Sep 18 2013: (Start)

%F G.f.: x*(1 + 7*x - x^2)/((1+x)*(x-1)^2).

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

%F a(n) = (14*n + 7*(-1)^n - 3)/4. (End)

%F a(n) = A168333(n) - 1 = A168374(n) + 1. - _Bruno Berselli_, Sep 18 2013

%F E.g.f.: (1/2)*(-2 + (7*x + 2)*cosh(x) + (7*x - 5)*sinh(x)). - _G. C. Greubel_, Jul 18 2016

%t Table[ 1 + 7*floor(n/2) , {n,60}] (* _Bruno Berselli_, Sep 18 2013 *)

%t CoefficientList[Series[(1 + 7 x - x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 18 2013 *)

%o (Magma) [7*n/2 + 7*(-1)^n/4 - 3/4: n in [1..70]]; // _Vincenzo Librandi_, Sep 18 2013

%Y Cf. A016993, A168333, A168374.

%K nonn,easy,less

%O 1,2

%A _Vincenzo Librandi_, Nov 23 2009

%E New definition by _Bruno Berselli_, Sep 18 2013