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 A288599 a(n) = 2*a(n-1) - a(n-4) for n >= 4, where a(0) = 2, a(1) = 4, a(2) = 6, a(3) = 10, a(4) = 16. 2

%I

%S 2,4,6,10,16,28,50,90,164,300,550,1010,1856,3412,6274,11538,21220,

%T 39028,71782,132026,242832,446636,821490,1510954,2779076,5111516,

%U 9401542,17292130,31805184,58498852,107596162,197900194,363995204,669491556,1231386950

%N a(n) = 2*a(n-1) - a(n-4) for n >= 4, where a(0) = 2, a(1) = 4, a(2) = 6, a(3) = 10, a(4) = 16.

%C Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iteration of the mapping 00->0101, 10->1000, starting with 00; see A288596.

%H Clark Kimberling, <a href="/A288599/b288599.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, 0, -1).

%F a(n) = 2*a(n-1) - a(n-4) for n >= 4, where a(0) = 2, a(1) = 4, a(2) = 6, a(3) = 10, a(4) = 16.

%F G.f.: -((2*(-1 + x^2 + x^3 + x^4))/(1 - 2*x + x^4)).

%t Join[{2}, LinearRecurrence[{2, 0, 0, -1}, {4, 6, 10, 16}, 40]]

%Y Cf. A288596.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Jun 14 2017

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Last modified December 8 14:18 EST 2021. Contains 349596 sequences. (Running on oeis4.)