A166033 - OEIS

%I #23 Sep 08 2022 08:45:48

%S 1,21,12,32,23,43,34,54,45,65,56,76,67,87,78,98,89,109,100,120,111,

%T 131,122,142,133,153,144,164,155,175,166,186,177,197,188,208,199,219,

%U 210,230,221,241,232,252,243,263,254,274,265,285,276,296,287,307,298,318

%N a(n) = 11/4 +11*n/2 + 29*(-1)^n/4.

%H Vincenzo Librandi, <a href="/A166033/b166033.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) = 11*n-a(n-1) with n>1, a(1)=1.

%F G.f.: -x*(-1-20*x+10*x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Jan 05 2011

%F E.g.f.: (1/2)*((11*x + 20)*cosh(x) + (11*x - 9)*sinh(x) - 20). - _G. C. Greubel_, Apr 24 2016

%t Table[11/4+11*n/2+29*(-1)^n/4,{n,1,60}] (* or *) LinearRecurrence[{1,1,-1},{1,21,12},60] (* _Vincenzo Librandi_, Mar 14 2012 *)

%o (Magma) [11/4+11*n/2+29*(-1)^n/4: n in [1..60]]; // _Vincenzo Librandi_, Mar 14 2012

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Oct 16 2009

%E New definition from _R. J. Mathar_, Jan 05 2011