A168420 - OEIS

%I #25 Mar 04 2024 01:13:20

%S 4,14,14,24,24,34,34,44,44,54,54,64,64,74,74,84,84,94,94,104,104,114,

%T 114,124,124,134,134,144,144,154,154,164,164,174,174,184,184,194,194,

%U 204,204,214,214,224,224,234,234,244,244,254,254,264,264,274,274,284

%N a(n) = 4 + 10*floor(n/2).

%H Vincenzo Librandi, <a href="/A168420/b168420.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) = 10*n - a(n-1) - 2, with n>1, a(1)=4.

%F G.f.: 2*x*(2 + 5*x - 2*x^2)/((1+x)*(x-1)^2). - _Vincenzo Librandi_, Sep 19 2013

%F a(n) = a(n-1) +a(n-2) -a(n-3). - _Vincenzo Librandi_, Sep 19 2013

%F a(n) = 2*A168278(n). - _Bruno Berselli_, Sep 19 2013

%F E.g.f.: (1/2)*(5 - 8*exp(x) + (10*x + 3)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 22 2016

%t Table[4 + 10 Floor[n/2], {n, 70}] (* or *) CoefficientList[Series[(4 + 10 x - 4 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 19 2013 *)

%o (Magma) [4+10*Floor(n/2): n in [1..70]]; // _Vincenzo Librandi_, Sep 19 2013

%Y Cf. A017317, A168278.

%K nonn,easy,less

%O 1,1

%A _Vincenzo Librandi_, Nov 25 2009

%E New definition by _Vincenzo Librandi_, Sep 19 2013