login
A308189
Numbers of the form t_n or t_n + t_{n+1} where {t_n} are the tribonacci numbers A000073.
1
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
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.
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jun 09 2019
STATUS
approved