A168206 - OEIS

%I #27 Feb 23 2023 03:46:02

%S 0,11,5,16,10,21,15,26,20,31,25,36,30,41,35,46,40,51,45,56,50,61,55,

%T 66,60,71,65,76,70,81,75,86,80,91,85,96,90,101,95,106,100,111,105,116,

%U 110,121,115,126,120,131,125,136,130,141,135,146,140,151,145,156,150,161

%N a(n) = 5*n - a(n-1) + 1 with n>1, a(1)=0.

%H Vincenzo Librandi, <a href="/A168206/b168206.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 + 7 + 17*(-1)^n)/4. - _Jon E. Schoenfield_, Jun 24 2010

%F G.f.: x^2*(11-6*x)/((1+x)*(1-x)^2). - _Vincenzo Librandi_, Feb 28 2012

%F E.g.f.: (1/4)*(17 - 24*exp(x) + (7 + 10*x)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 15 2016

%F Sum_{n>=2} (-1)^(n+1)/a(n) = 7/6 - log(5)/4 - log(phi)/(2*sqrt(5)) - sqrt(1+2/sqrt(5))*Pi/10, where phi is the golden ratio (A001622). - _Amiram Eldar_, Feb 23 2023

%t LinearRecurrence[{1, 1, -1}, {0, 11, 5}, 30] (* _Vincenzo Librandi_, Feb 28 2012 *)

%o (Magma) I:=[0, 11, 5]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Feb 28 2012

%Y Cf. A001622.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Nov 20 2009