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a(n) = 2*(10*3^n - 1).
1

%I #21 Sep 08 2022 08:45:40

%S 18,58,178,538,1618,4858,14578,43738,131218,393658,1180978,3542938,

%T 10628818,31886458,95659378,286978138,860934418,2582803258,7748409778,

%U 23245229338,69735688018,209207064058,627621192178,1882863576538

%N a(n) = 2*(10*3^n - 1).

%H Vincenzo Librandi, <a href="/A155155/b155155.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).

%F a(n) = 4*a(n-1) - 3*a(n-2).

%F G.f.: ( 18 - 14*x ) / ( (1-x)*(1-3*x) ).

%F a(n) = 10*A048473(n) + 8 = A048473(n) + A048473(n+2).

%F a(n) = 3*a(n-1) - a(n-2) + 3*a(n-3) + 8.

%F From _G. C. Greubel_, Mar 20 2021: (Start)

%F a(n) = 18*A003462(n+1) - 14*A003462(n).

%F E.g.f.: 2*( 10*exp(3*x) - exp(x) ). (End)

%F a(n) = 2 * A198645(n). - _Joerg Arndt_, Mar 21 2021

%p seq(2*(10*3^n -1), n=0..30); # _G. C. Greubel_, Mar 20 2021

%t 2*(10*3^Range[0,30] -1) (* _G. C. Greubel_, Mar 20 2021 *)

%o (Magma) [2*(10*3^n-1): n in [0..30]]; // _Vincenzo Librandi_, Aug 07 2011

%o (Sage) [2*(10*3^n - 1) for n in (0..30)] # _G. C. Greubel_, Mar 20 2021

%Y Cf. A003462, A048473.

%K nonn,easy,less

%O 0,1

%A _Paul Curtz_, Jan 21 2009