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%I #21 Mar 02 2022 12:08:47
%S 1,6,66,666,6306,58026,527346,4766586,42981186,387158346,3485735826,
%T 31376865306,282412759266,2541798719466,22876524019506,
%U 205890058352826,1853015893884546,16677164519797386,150094566577522386
%N a(n) = 9^n-4^n+1^n.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14,-49,36).
%F G.f.: 1/(1-9*x)-1/(1-4*x)+1/(1-x). E.g.f.: e^(9*x)-e^(4*x)+e^x.
%F a(n) = 13*a(n-1)-36*a(n-2)+24 with a(0)=1, a(1)=6. - _Vincenzo Librandi_, Jul 21 2010
%t Table[9^n-4^n+1,{n,0,20}] (* or *) LinearRecurrence[{14,-49,36},{1,6,66},20] (* _Harvey P. Dale_, Aug 08 2019 *)
%o (PARI) a(n)=9^n-4^n+1 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624, A155625, A155626, A155627, A155628, A155629.
%K nonn,easy
%O 0,2
%A _Mohammad K. Azarian_, Jan 30 2009
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