A228925 Stern's triatomic sequence.

1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 5, 1, 3, 5, 3, 1, 5, 1, 1, 5, 1, 3, 5, 3, 1, 5, 1, 1, 5, 1, 3, 5, 3, 1, 5, 1, 1, 7, 1, 5, 7, 5, 1, 7, 1, 3, 9, 3, 5, 9, 5, 1, 9, 3, 1, 9, 1, 5, 9, 5, 3, 9, 1, 1, 7, 1, 5, 7, 5, 1, 7, 1, 3, 9, 3, 5, 9, 5, 1, 9, 3, 1, 9, 1, 5, 9, 5, 3, 9, 1, 1, 7, 1, 5, 7, 5

Offset

0,6

Links

Table of n, a(n) for n=0..99.

Thomas Garrity, "A Multidimensional Continued Fraction Generalization of Stern's Diatomic Sequence", J. Integer Sequence 13 (2013), Paper 13.7.7

Formula

Satisfies the recurrence relations

a(9n+3) = a(3n)

a(9n+4) = a(3n+1)

a(9n+5) = a(3n)+a(3n+1)+a(3n+2)

a(9n+6) = a(3n+1)

a(9n+7) = a(3n+2)

a(9n+8) = a(3n)+a(3n+1)+a(3n+2)

a(27n) = a(9n+2)

a(27n+2) = -a(9n+1)+2a(9n+2)

a(27n+9) = a(9n+2)

a(27n+10) = a(9n)

a(27n+11) = a(9n)+a(9n+1)+a(9n+2)

a(27n+18) = a(3n)+a(3n+1)+a(3n+2)

a(27n+19) = a(3n)

a(27n+20) = 2a(3n) + 2a(3n+1) + a(3n+2)

a(81n+1) = a(9n)

a(81n+28) = a(9n+1)

a(81n+55) = a(3n+1) for n >= 0.

Crossrefs

Cf. A002487.

Sequence in context: A353517 A353487 A356308 * A230405 A101685 A238737

Adjacent sequences: A228922 A228923 A228924 * A228926 A228927 A228928

Keyword

nonn

Author

Jeffrey Shallit, Sep 08 2013

Status

approved