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%I #13 Apr 07 2020 23:10:58
%S 2,4,7,11,17,25,36,51,70,93,120,151,186,225,268,315,366,421,480,543,
%T 610,681,756,835,918,1005,1096,1191,1290,1393,1500,1611,1726,1845,
%U 1968,2095,2226,2361,2500,2643,2790,2941,3096,3255,3418,3585,3756,3931,4110
%N a(n) = 3*a(n-1) - 3*a(n-2) + *a(n-3) for n >= 8, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 11, a(4) = 17, a(5) = 25, a(6) = 36, a(7) = 51.
%C Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iterate of the mapping 00->0010, 01->010, 10->011, starting with 00; see A289057.
%H Clark Kimberling, <a href="/A289060/b289060.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 8, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 11, a(4) = 17, a(5) = 25, a(6) = 36, a(7) = 51.
%F G.f.: (-2 + 2*x - x^2 - x^4 - x^6 - x^7)/(-1 + x)^3.
%F a(n) = 30 - 11*n + 2*n^2 for n>4. - _Colin Barker_, Jul 02 2017
%t Join[{2, 4, 7, 11, 17}, LinearRecurrence[{3, -3, 1}, {25, 36, 51}, 40]]
%Y Cf. A288216.
%K nonn,easy
%O 0,1
%A _Clark Kimberling_, Jun 27 2017
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