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%I #37 Jun 24 2020 09:06:35
%S 1,3,7,14,27,51,95,176,325,599,1103,2030,3735,6871,12639,23248,42761,
%T 78651,144663,266078,489395,900139,1655615,3045152,5600909,10301679,
%U 18947743,34850334,64099759,117897839,216847935,398845536
%N G.f.: x^2*(x^2 + x + 1)/(x^4 - 2*x + 1).
%C Lengths of palindromic prefixes of the ternary tribonacci word A080843 [A. Glen]. - _N. J. A. Sloane_, Jun 09 2019
%C Original definition was: a(n) = (1/2)*T(n,n+2), T given by A027082.
%H Hamoon Mousavi, 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 Bo Tan and Zhi-Ying Wen, <a href="http://dx.doi.org/10.1016/j.ejc.2006.07.007">Some properties of the Tribonacci sequence</a>, European Journal of Combinatorics, 28 (2007) 1703-1719. See Prop. 2.9, |D_n|.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, 0, -1).
%F Positive numbers of the form (t_n + t_{n+2} - 3)/2, n>1, where {t_n} are the tribonacci numbers A000073 [A. Glen]. See Mousavi-Shallit, 2014. - _N. J. A. Sloane_, Jun 09 2019
%F a(n) = A008937(n-1) - 1 = A018921(n-3) - 1.
%F 2*a(n) = A000213(n+2)-3. - _R. J. Mathar_, Jun 24 2020
%o (PARI) Vec(x^2*(x^2 + x + 1)/(x^4 - 2*x + 1) + O(x^50)) \\ _Michel Marcus_, Dec 29 2014
%Y Cf. A000073, A008937, A018921, A027082, A080843, A317197 (D_n).
%K nonn,easy
%O 2,2
%A _Clark Kimberling_
%E Entry revised by _N. J. A. Sloane_, Aug 05 2018
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