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a(n) = 4^n-3*n+1.
1

%I #33 Oct 13 2024 17:42:16

%S 2,2,11,56,245,1010,4079,16364,65513,262118,1048547,4194272,16777181,

%T 67108826,268435415,1073741780,4294967249,17179869134,68719476683,

%U 274877906888,1099511627717,4398046511042,17592186044351,70368744177596

%N a(n) = 4^n-3*n+1.

%H Vincenzo Librandi, <a href="/A175976/b175976.txt">Table of n, a(n) for n = 0..250</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,4).

%F G.f.: ( -2+10*x-17*x^2 ) / ( (4*x-1)*(x-1)^2 ).

%F From _Bruno Berselli_, Nov 04 2010: (Start)

%F a(n)-6*a(n-1)+9*a(n-2)-4*a(n-3) = 0 for n>2.

%F a(n) = A158879(n)-A131098(n+1) (n>0). (End)

%e a(1)=4-3+1=2. a(2)=16-6+1=11.

%p A175976 := proc(n) 4^n-3*n+1 ; end proc:

%t Table[4^n-3n+1,{n,0,30}] (* or *) LinearRecurrence[{6,-9,4},{2,2,11},30] (* _Harvey P. Dale_, Jul 07 2013 *)

%o (Magma) [4^n-3*n+1: n in [0..30]]; // _Vincenzo Librandi_, Mar 20 2014

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Nov 02 2010

%E G.f., program and link to recurrences from _R. J. Mathar_, Nov 03 2010