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A278038 Binary vectors not containing three consecutive 1's; or, representation of n in the tribonacci base. 32
0, 1, 10, 11, 100, 101, 110, 1000, 1001, 1010, 1011, 1100, 1101, 10000, 10001, 10010, 10011, 10100, 10101, 10110, 11000, 11001, 11010, 11011, 100000, 100001, 100010, 100011, 100100, 100101, 100110, 101000, 101001, 101010, 101011, 101100, 101101, 110000, 110001, 110010, 110011, 110100, 110101, 110110, 1000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

These are the nonnegative numbers written in the tribonacci numbering system.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..25280

F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, arXiv:1907.09120, July 2019

Eric DuchĂȘne and Michel Rigo, A morphic approach to combinatorial games: the Tribonacci case. RAIRO - Theoretical Informatics and Applications, 42, 2008, pp 375-393. See Table 2. [Also available from Numdam]

Wolfdieter Lang, The Tribonacci and ABC Representations of Numbers are Equivalent, arXiv preprint arXiv:1810.09787 [math.NT], 2018.

EXAMPLE

The tribonacci numbers (as in A000073(n), for n >= 3) are 1, 2, 4, 7, 13, 24, 44, 81, ... In terms of this base, 7 is written 1000, 8 is 1001, 11 is 1100, 12 is 1101, 13 is 10000, etc. Zero is 0.

CROSSREFS

Cf. A000073, A080843 (Tribonacci word, tribonacci tree).

See A003726 for the decimal representations of these binary strings.

Sequence in context: A066334 A136829 A262381 * A136832 A136808 A136836

Adjacent sequences:  A278035 A278036 A278037 * A278039 A278040 A278041

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Nov 16 2016

STATUS

approved

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Last modified January 18 13:30 EST 2020. Contains 331007 sequences. (Running on oeis4.)