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%I #31 Jun 30 2023 16:47:07
%S 16,40,88,184,376,760,1528,3064,6136,12280,24568,49144,98296,196600,
%T 393208,786424,1572856,3145720,6291448,12582904,25165816,50331640,
%U 100663288,201326584,402653176,805306360,1610612728,3221225464,6442450936,12884901880
%N a(n) = 3*a(n-1) - 2*a(n-2) with a(0)=16 and a(1)=40.
%C Number of vertices into building blocks of 3d objects with 4 vertices.
%H Vincenzo Librandi, <a href="/A182461/b182461.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 + 8.
%F G.f.: 16 + 40*x + 88*x^2 + 184*x^3 + 376*x^4 + 760*x^5 + 1528*x^6 + ...
%F a(n) = 8 * A055010(n+1). [_Joerg Arndt_, Jun 01 2014]
%F G.f.: -((8*(x - 2))/(2*x^2 - 3*x + 1)). - _Vincenzo Librandi_, Jun 02 2014
%e a(0) = 4+8+4;
%e a(1) = 4+8+16+8+4;
%e a(2) = 4+8+16+32+16+8+4;
%e a(3) = 4+8+16+32+64+32+16+8+4.
%t CoefficientList[Series[-((8 (x - 2))/(2 x^2 - 3 x + 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 02 2014 *)
%Y Cf. A000045, A028399, A038578, A089143, A173033, A182462, A182464, A182465, A182466, A182467.
%K nonn,easy
%O 0,1
%A _Odimar Fabeny_, Apr 30 2012
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