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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 (list; graph; refs; listen; history; text; internal format)
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, 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)

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

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)