

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
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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: nonattacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.
Eric DuchĂȘne and Michel Rigo, A morphic approach to combinatorial games: the Tribonacci case. RAIRO  Theoretical Informatics and Applications, 42, 2008, pp 375393. 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



