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6^n - 3^n + 1.
9

%I #14 Jun 13 2015 00:52:47

%S 1,4,28,190,1216,7534,45928,277750,1673056,10058014,60407128,

%T 362619910,2176250896,13059099694,78359381128,470170635670,

%U 2821066860736,16926530304574,101559569247928,609358577749030,3656154953278576

%N 6^n - 3^n + 1.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (10,-27,18).

%F G.f.: 1/(1-6*x)-1/(1-3*x)+1/(1-x). E.g.f.: e^(6*x)-e^(3*x)+e^x.

%F a(n)=9*a(n-1)-18*a(n-2)+10 with a(0)=1, a(1)=4 [From _Vincenzo Librandi_, Jul 21 2010]

%F E.g.f.: exp(6*x)-exp(3*x)+exp(x)= G(0) ; G(k)= 1 - 1/( 2^k + 2^k/( 3^k - 1 - 6*x*18^k/( x*6^(k+1)+(k+1)/G(k+1)))); (continued fraction, 3-step ). - Sergei N. Gladkovskii, Jan 10 2012

%o (PARI) a(n)=6^n-3^n+1 \\ _Charles R Greathouse IV_, Jan 09 2012

%Y Cf. A155596-A155610.

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_, Jan 26 2009