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%I #15 Apr 07 2020 21:22:06
%S 2,4,7,11,18,31,52,89,151,257,438,748,1277,2179,3719,6348,10837,18499,
%T 31579,53908,92027,157099,268182,457812,781531,1334153,2277532,
%U 3887973,6637157,11330291,19341939,33018621,56366084,96222539,164261491,280410777,478689212
%N a(n) = 2*a(n-1) - a(n-2) + 2*a(n-4) - a(n-5) + a(n-7) - a(n-8) - a(n-10) for n >= 10, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 11, a(4) = 18, a(5) = 31, a(6) = 52, a(7) = 89, a(9) = 151, a(9) = 257.
%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->001, 10->010, starting with 00; see A289001.
%H Clark Kimberling, <a href="/A289004/b289004.txt">Table of n, a(n) for n = 0..2000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,2,-1,0,1,-1,0,-1).
%F a(n) = 2*a(n-1) - a(n-2) + 2*a(n-4) - a(n-5) + a(n-7) - a(n-8) - a(n-10) for n >= 10, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 11, a(4) = 18, a(5) = 31, a(6) = 52, a(7) = 89, a(9) = 151, a(9) = 257.
%F G.f.: (2 + x^2 + x^3 - x^4 - 2*x^6 - x^7 - 2*x^8 - 3*x^9) / ((1 - x)*(1 - x - 2*x^4 - x^5 - x^6 - 2*x^7 - x^8 - x^9)). - _Colin Barker_, Jun 26 2017
%t LinearRecurrence[{2, -1, 0, 2, -1, 0, 1, -1, 0, -1}, {2, 4, 7, 11, 18, 31, 52, 89, 151, 257}, 20]
%o (PARI) Vec((2 + x^2 + x^3 - x^4 - 2*x^6 - x^7 - 2*x^8 - 3*x^9) / ((1 - x)*(1 - x - 2*x^4 - x^5 - x^6 - 2*x^7 - x^8 - x^9)) + O(x^40)) \\ _Colin Barker_, Jun 26 2017
%Y Cf. A288216.
%K nonn,easy
%O 0,1
%A _Clark Kimberling_, Jun 26 2017
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