login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

a(n) = a(n-1) + a(n-2) + a(n-3) - 2*a(n-4) for n >= 5, where a(0) = 2, a(1) = 4, a(2) = 5, a(3) = 8, a(4) = 11.
3

%I #11 Apr 07 2020 21:37:35

%S 2,4,5,8,11,16,25,36,55,84,125,192,291,440,673,1020,1551,2364,3589,

%T 5464,8315,12640,19241,29268,44519,67748,103053,156784,238547,362888,

%U 552113,839980,1277887,1944204,2957845,4499976,6846251,10415664,15846201,24108164

%N a(n) = a(n-1) + a(n-2) + a(n-3) - 2*a(n-4) for n >= 5, where a(0) = 2, a(1) = 4, a(2) = 5, a(3) = 8, a(4) = 11.

%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->010, starting with 00; see A288520.

%H Clark Kimberling, <a href="/A288523/b288523.txt">Table of n, a(n) for n = 0..10000</a>

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

%F a(n) = a(n-1) + a(n-2) + a(n-3) - 2*a(n-4) for n >= 5, where a(0) = 2, a(1) = 4, a(2) = 5, a(3) = 8, a(4) = 11.

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

%t Join[{2}, LinearRecurrence[{1, 1, 1, -2}, {4, 5, 8, 11}, 40]]

%Y Cf. A288520.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Jun 13 2017