A027084 G.f.: x^2*(x^2 + x + 1)/(x^4 - 2*x + 1).

1, 3, 7, 14, 27, 51, 95, 176, 325, 599, 1103, 2030, 3735, 6871, 12639, 23248, 42761, 78651, 144663, 266078, 489395, 900139, 1655615, 3045152, 5600909, 10301679, 18947743, 34850334, 64099759, 117897839, 216847935, 398845536

Offset: 2

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

Lengths of palindromic prefixes of the ternary tribonacci word A080843 [A. Glen]. - N. J. A. Sloane, Jun 09 2019

Original definition was: a(n) = (1/2)*T(n,n+2), T given by A027082.

Links

• Hamoon Mousavi, Jeffrey Shallit, Mechanical Proofs of Properties of the Tribonacci Word, arXiv:1407.5841 [cs.FL], 2014.
• Bo Tan and Zhi-Ying Wen, Some properties of the Tribonacci sequence, European Journal of Combinatorics, 28 (2007) 1703-1719. See Prop. 2.9, |D_n|.
• Index entries for linear recurrences with constant coefficients, signature (2, 0, 0, -1).

Crossrefs

Cf. A000073, A008937, A018921, A027082, A080843, A317197 (D_n).

Programs

PARI

Vec(x^2*(x^2 + x + 1)/(x^4 - 2*x + 1) + O(x^50)) \\ Michel Marcus, Dec 29 2014

Formula

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

a(n) = A008937(n-1) - 1 = A018921(n-3) - 1.

2*a(n) = A000213(n+2)-3. - R. J. Mathar, Jun 24 2020

Extensions

Entry revised by N. J. A. Sloane, Aug 05 2018