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8^n - 3^n + 1.
7

%I #15 Oct 07 2015 11:32:34

%S 1,6,56,486,4016,32526,261416,2094966,16770656,134198046,1073682776,

%T 8589757446,68718945296,549754219566,4398041728136,35184357739926,

%U 281474933663936,2251799684545086,18014398122061496,144115186913594406

%N 8^n - 3^n + 1.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (12,-35,24).

%F G.f.: 1/(1-8*x)-1/(1-3*x)+1/(1-x).

%F E.g.f.: e^(8*x)-e^(3*x)+e^x.

%F a(n) = 11*a(n-1)-24*a(n-2)+14 with a(0)=1, a(1)=6. - _Vincenzo Librandi_, Jul 21 2010

%t Table[8^n-3^n+1,{n,0,20}] (* or *) LinearRecurrence[{12,-35,24},{1,6,56},20] (* _Harvey P. Dale_, Mar 12 2014 *)

%o (PARI) a(n)=8^n-3^n+1 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608, A155609, A155610, A155611, A155612.

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_, Jan 26 2009