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A308189 Numbers of the form t_n or t_n + t_{n+1} where {t_n} are the tribonacci numbers A000073.

%I A308189 #28 Nov 14 2023 08:09:48
%S A308189 0,1,2,3,4,6,7,11,13,20,24,37,44,68,81,125,149,230,274,423,504,778,
%T A308189 927,1431,1705,2632,3136,4841,5768,8904,10609,16377,19513,30122,35890,
%U A308189 55403,66012,101902,121415,187427,223317,344732,410744,634061,755476,1166220,1389537,2145013,2555757,3945294,4700770,7256527
%N A308189 Numbers of the form t_n or t_n + t_{n+1} where {t_n} are the tribonacci numbers A000073.
%C A308189 Orders of squares in the ternary tribonacci word A080843.
%C A308189 This is A213816 with duplicates removed.
%H A308189 Colin Barker, <a href="/A308189/b308189.txt">Table of n, a(n) for n = 1..1000</a>
%H A308189 Hamoon Mousavi and Jeffrey Shallit, <a href="https://arxiv.org/abs/1407.5841">Mechanical Proofs of Properties of the Tribonacci Word</a>, arXiv:1407.5841 [cs.FL], 2014.
%H A308189 H. Mousavi and J. Shallit, <a href="https://doi.org/10.1007/978-3-319-23660-5_15">Mechanical Proofs of Properties of the Tribonacci Word</a>, In: Manea F., Nowotka D. (eds) Combinatorics on Words. WORDS 2015. Lecture Notes in Computer Science, vol 9304. Springer, 2015, pp. 170-190.
%H A308189 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,1,0,1).
%F A308189 From _Colin Barker_, Jun 11 2019: (Start)
%F A308189 G.f.: x^2*(1 + 2*x + 2*x^2 + 2*x^3 + 2*x^4 + x^5 + x^6) / (1 - x^2 - x^4 - x^6).
%F A308189 a(n) = a(n-2) + a(n-4) + a(n-6) for n>8.
%F A308189 (End)
%t A308189 LinearRecurrence[{0,1,0,1,0,1},{0,1,2,3,4,6,7,11},100] (* _Paolo Xausa_, Nov 14 2023 *)
%o A308189 (PARI) concat(0, Vec(x^2*(1 + 2*x + 2*x^2 + 2*x^3 + 2*x^4 + x^5 + x^6) / (1 - x^2 - x^4 - x^6) + O(x^50))) \\ _Colin Barker_, Jun 11 2019
%Y A308189 Cf. A000073, A001590, A080843, A092782, A213816.
%K A308189 nonn,easy
%O A308189 1,3
%A A308189 _N. J. A. Sloane_, Jun 09 2019