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a(n) = 3*9^n-1.
1

%I #31 Dec 08 2024 10:19:15

%S 2,26,242,2186,19682,177146,1594322,14348906,129140162,1162261466,

%T 10460353202,94143178826,847288609442,7625597484986,68630377364882,

%U 617673396283946,5559060566555522,50031545098999706,450283905890997362

%N a(n) = 3*9^n-1.

%H Vincenzo Librandi, <a href="/A198960/b198960.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (10,-9).

%F a(n) = 2*A096053(n).

%F a(n) = 9*a(n-1)+8, n>0.

%F a(n) = 10*a(n-1)-9*a(n-2), n>1.

%F G.f.: 2*(1 + 3*x)/(1 - 10*x + 9*x^2). - _Vincenzo Librandi_, Jan 03 2013

%t CoefficientList[Series[2*(1 + 3*x)/(1 - 10*x + 9*x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jan 03 2013 *)

%t LinearRecurrence[{10,-9},{2,26},30] (* _Harvey P. Dale_, Dec 07 2024 *)

%o (Magma) [3*9^n-1: n in [0..20]];

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Nov 01 2011