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

Author

N. J. A. Sloane, Jun 09 2019

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

Mathematica

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

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

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)