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

0, 1, 2, 3, 4, 6, 7, 11, 13, 20, 24, 37, 44, 68, 81, 125, 149, 230, 274, 423, 504, 778, 927, 1431, 1705, 2632, 3136, 4841, 5768, 8904, 10609, 16377, 19513, 30122, 35890, 55403, 66012, 101902, 121415, 187427, 223317, 344732, 410744, 634061, 755476, 1166220, 1389537, 2145013, 2555757, 3945294, 4700770, 7256527

Offset

1,3

Comments

Orders of squares in the ternary tribonacci word A080843.

This is A213816 with duplicates removed.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Hamoon Mousavi and Jeffrey Shallit, Mechanical Proofs of Properties of the Tribonacci Word, arXiv:1407.5841 [cs.FL], 2014.

H. Mousavi and J. Shallit, Mechanical Proofs of Properties of the Tribonacci Word, In: Manea F., Nowotka D. (eds) Combinatorics on Words. WORDS 2015. Lecture Notes in Computer Science, vol 9304. Springer, 2015, pp. 170-190.

Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,0,1).

Formula

From Colin Barker, Jun 11 2019: (Start)

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).

a(n) = a(n-2) + a(n-4) + a(n-6) for n>8.

(End)

Mathematica

LinearRecurrence[{0, 1, 0, 1, 0, 1}, {0, 1, 2, 3, 4, 6, 7, 11}, 100] (* Paolo Xausa, Nov 14 2023 *)

Prog

(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

Crossrefs

Cf. A000073, A001590, A080843, A092782, A213816.

Sequence in context: A202113 A113243 A130690 * A074885 A215231 A301512

Adjacent sequences: A308186 A308187 A308188 * A308190 A308191 A308192

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 09 2019

Status

approved