%I #23 Sep 08 2022 08:45:49
%S 5,5,12,12,19,19,26,26,33,33,40,40,47,47,54,54,61,61,68,68,75,75,82,
%T 82,89,89,96,96,103,103,110,110,117,117,124,124,131,131,138,138,145,
%U 145,152,152,159,159,166,166,173,173,180,180,187,187,194,194,201,201,208
%N a(n) = 5 + 7*floor((n-1)/2).
%H Vincenzo Librandi, <a href="/A168336/b168336.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) - 4, with n>1, a(1)=5.
%F G.f.: x*(5 + 2*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) = (14*n - 7*(-1)^n - 1)/4. - _Bruno Berselli_, Sep 18 2013
%F a(n) = A168332(n) - 1 = A168373(n) + 1. - _Bruno Berselli_, Sep 18 2013
%F E.g.f.: (1/2)*(4 + (7*x - 4)*cosh(x) + (7*x + 3)* sinh(x)). - _G. C. Greubel_, Jul 18 2016
%t Table[5 + 7 Floor[(n - 1)/2], {n, 60}] (* _Bruno Berselli_, Sep 18 2013 *)
%t CoefficientList[Series[(5 + 2 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 18 2013 *)
%o (Magma) [5+7*Floor((n-1)/2): n in [1..70]]; // _Vincenzo Librandi_, Sep 18 2013
%Y Cf. A017041, A168332, A168373.
%K nonn,easy,less
%O 1,1
%A _Vincenzo Librandi_, Nov 23 2009
%E New definition by _Vincenzo Librandi_, Sep 18 2013
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