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A288476 a(n) = a(n-1) + 4*a(n-2) - 2*a(n-3), where a(0) = 2, a(1) = 4, a(2) = 8. 5

%I

%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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Last modified April 22 14:20 EDT 2021. Contains 343177 sequences. (Running on oeis4.)