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%I #11 Apr 06 2020 20:12:38
%S 2,3,6,10,17,29,51,90,160,282,499,881,1559,2758,4880,8634,15275,27025,
%T 47815,84598,149680,264826,468555,829009,1466759,2595126,4591536,
%U 8123770,14373323,25430609,44994183,79607862,140849584,249204090,440914891,780107345
%N a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) + 2*a(n-5) - 2*a(n-7) for n>7 and where a(0)=2, a(1)=3, a(2)=6, a(3)=10, a(4)=17, a(5)=29, a(6)=51.
%C Conjecture: a(n) is the number of letters (0's and 1's) in the n-th iteration of the mapping 00->001, 1->000, starting with 00; see A286939.
%H Clark Kimberling, <a href="/A285665/b285665.txt">Table of n, a(n) for n = 0..3000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,-1,2,0,-2).
%F G.f.: (2 + x - x^2 - 3*x^5 - 2*x^6)/(1 - x - 2*x^2 + x^3 + x^4 - 2*x^5 + 2 x^7) = (2 + x - x^2 - 3*x^5 - 2*x^6)/((1 - x)*(1 + x)*(1 - x + x^2)*(1 - 2*x^2 - 2*x^3)).
%t LinearRecurrence[{1, 2, -1, -1, 2, 0, -2}, {2, 3, 6, 10, 17, 29, 51}, 40]
%Y Cf. A286939.
%K nonn,easy
%O 0,1
%A _Clark Kimberling_, Jun 05 2017
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