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a(n) = 4 + 9*floor(n/2).
1

%I #22 Mar 04 2024 01:12:29

%S 4,13,13,22,22,31,31,40,40,49,49,58,58,67,67,76,76,85,85,94,94,103,

%T 103,112,112,121,121,130,130,139,139,148,148,157,157,166,166,175,175,

%U 184,184,193,193,202,202,211,211,220,220,229,229,238,238,247,247,256,256

%N a(n) = 4 + 9*floor(n/2).

%H Vincenzo Librandi, <a href="/A168401/b168401.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) = 9*n - a(n-1) - 1, with n > 1, a(1)=4.

%F G.f.: x*(4 + 9*x - 4*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 E.g.f.: (1/4)*(9 - 16*exp(x) + (7 + 18*x)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 21 2016

%t Table[4 + 9 Floor[n/2], {n, 60}] (* _Vincenzo Librandi_, Sep 18 2013 *)

%o (Magma) [4+9*Floor(n/2): n in [1..60]]; // _Bruno Berselli_, Sep 18 2013

%o (PARI) a(n)=n\2*9 + 4 \\ _Charles R Greathouse IV_, Jul 21 2016

%Y Cf. A017209.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Nov 25 2009

%E New definition by _Vincenzo Librandi_ Sep 18 2013