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9^n - 3^n + 1.
6

%I #18 Oct 07 2015 15:08:38

%S 1,7,73,703,6481,58807,530713,4780783,43040161,387400807,3486725353,

%T 31380882463,282429005041,2541864234007,22876787671993,

%U 205891117745743,1853020145805121,16677181570526407,150094634909578633

%N 9^n - 3^n + 1.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (13,-39,27).

%F G.f.: 1/(1-9*x)-1/(1-3*x)+1/(1-x).

%F E.g.f.: e^(9*x)-e^(3*x)+e^x.

%F a(n) = 12*a(n-1)-27*a(n-2)+16 with a(0)=1, a(1)=7. - _Vincenzo Librandi_, Jul 21 2010

%t Table[9^n-3^n+1,{n,0,20}] (* _Harvey P. Dale_, Feb 03 2011 *)

%o (PARI) a(n)=9^n-3^n+1 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608, A155609, A155610, A155611, A155612, A155613.

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_, Jan 26 2009