%I #31 Sep 08 2022 08:45:24

%S 1,12,67,342,1717,8592,42967,214842,1074217,5371092,26855467,

%T 134277342,671386717,3356933592,16784667967,83923339842,419616699217,

%U 2098083496092,10490417480467,52452087402342,262260437011717,1311302185058592,6556510925292967

%N a(n) = (11*5^n - 7)/4.

%H Vincenzo Librandi, <a href="/A117088/b117088.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-5).

%F a(n) = 5*a(n-1) + 7 with a(0) = 1.

%F G.f.: (1+6*x)/((1-x)*(1-5*x)). - _Philippe Deléham_, Feb 22 2014

%F a(n) = 6*a(n-1) - 5*a(n-2), a(0) = 1, a(1) = 12. - _Philippe Deléham_, Feb 22 2014

%F a(n) = (11*5^n - 7) / 4. - _Ralf Stephan_, Feb 23 2014

%e If n=1 then 5*(n-1) + 7 = 5*1 + 7 = 12, which is the second term.

%p A117088:=n->(11*5^n-7)/4: seq(A117088(n), n=0..25); # _Wesley Ivan Hurt_, Nov 12 2014

%t NestList[5# + 7 &, 1, 50] (* _Stefan Steinerberger_, Apr 21 2006 *)

%o (Magma) [(11*5^n-7)/4 : n in [0..25]]; // _Wesley Ivan Hurt_, Nov 12 2014

%Y Cf. A117617, A116952.

%K nonn,easy

%O 0,2

%A _Parthasarathy Nambi_, Apr 17 2006

%E Definition corrected and better name by _Ralf Stephan_, Feb 23 2014