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a(n) = 3a(n-1) - 2a(n-2) with a(0)=20 and a(1)=50.
6

%I #22 Jun 30 2023 16:48:05

%S 20,50,110,230,470,950,1910,3830,7670,15350,30710,61430,122870,245750,

%T 491510,983030,1966070,3932150,7864310,15728630,31457270,62914550,

%U 125829110,251658230,503316470,1006632950,2013265910,4026531830,8053063670,16106127350

%N a(n) = 3a(n-1) - 2a(n-2) with a(0)=20 and a(1)=50.

%C Number of vertices into building blocks of 3d objects with 5 vertices.

%H Vincenzo Librandi, <a href="/A182462/b182462.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 (3, -2).

%F a(n) = a(n-1)*2 + 10.

%F a(n) = 10*A153893(n). - _Michel Marcus_, Jun 01 2014

%F G.f.: -((10*(x - 2))/(2*x^2 - 3*x + 1)). - _Vincenzo Librandi_, Jun 02 2014

%e a(0) = 5+10+5;

%e a(1) = 5+10+20+10+5;

%e a(2) = 5+10+20+40+20+10+5;

%e a(3) = 5+10+20+40+80+40+20+10+5.

%t CoefficientList[Series[-((10 (x - 2))/(2 x^2 - 3 x + 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 02 2014 *)

%Y Cf. A000045, A028399, A038578, A089143, A173033, A182461, A182464, A182465, A182466, A182467.

%K easy,nonn

%O 0,1

%A _Odimar Fabeny_, Apr 30 2012