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%I #8 Apr 06 2020 20:03:15
%S 2,4,8,20,44,108,244,588,1348,3212,7428,17580,40868,96332,224644,
%T 528236,1234148,2897804,6777924,15900844,37216932,87264460,204330500,
%U 478954476,1121747556,2628904460,6157985732,14430108460,33804242468,79208704844,185565457796
%N a(n) = a(n-1) + 4*a(n-2) - 2*a(n-3), where a(0) = 2, a(1) = 4, a(2) = 8.
%C Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iteration of the mapping 00->0101, 1->011, starting with 00; see A288473.
%H Clark Kimberling, <a href="/A288476/b288476.txt">Table of n, a(n) for n = 0..2000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 4, -2).
%F a(n) = a(n-1) + 4*a(n-2) - 2*a(n-3), where a(0) = 2, a(1) = 4, a(2) = 8.
%F G.f.: -((2*(-1 - x + 2*x^2))/(1 - x - 4*x^2 + 2*x^3)).
%t LinearRecurrence[{1, 4, -2}, {2, 4, 8}, 40]
%Y Cf. A288473.
%K nonn,easy
%O 0,1
%A _Clark Kimberling_, Jun 12 2017
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