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a(n) = (5*3^n + (-3)^n)/6.
1

%I #19 May 07 2024 03:22:59

%S 1,2,9,18,81,162,729,1458,6561,13122,59049,118098,531441,1062882,

%T 4782969,9565938,43046721,86093442,387420489,774840978,3486784401,

%U 6973568802,31381059609,62762119218,282429536481,564859072962

%N a(n) = (5*3^n + (-3)^n)/6.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,9).

%F From _Reinhard Zumkeller_, Mar 04 2011: (Start)

%F G.f.: (1+2x)/((1-3x)*(1+3x)).

%F E.g.f.: (5*exp(3x) + exp(-3x))/6.

%F a(n+3) = a(n+2)*a(n+1)/a(n). (End)

%F a(n) = 9*a(n-2). - _Vincenzo Librandi_, Mar 20 2011

%t LinearRecurrence[{0,9},{1,2},30] (* _Harvey P. Dale_, Dec 04 2019 *)

%Y Cf. A083424.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Apr 30 2003