A255723 Another variant of Per Nørgård's "infinity sequence", cf. A004718: t(0) = 0; t(4*n) = t(n); t(4*n+1) = t(n) - 2; t(4*n+2) = -t(n) - 1; t(4*n+3) = t(n) + 2.

0, -2, -1, 2, -2, -4, 1, 0, -1, -3, 0, 1, 2, 0, -3, 4, -2, -4, 1, 0, -4, -6, 3, -2, 1, -1, -2, 3, 0, -2, -1, 2, -1, -3, 0, 1, -3, -5, 2, -1, 0, -2, -1, 2, 1, -1, -2, 3, 2, 0, -3, 4, 0, -2, -1, 2, -3, -5, 2, -1, 4, 2, -5, 6, -2, -4, 1, 0, -4, -6, 3, -2, 1, -1

Offset: 0

Author

Reinhard Zumkeller, Mar 19 2015

Keywords

• sign

Comments

Per Nørgård's surname is also written as Noergaard;

example of a sequence sharing with A004718 some main characterizing properties, see link (chapter 7).

References

• Yu Hin (Gary) Au, Christopher Drexler-Lemire, and Jeffrey Shallit, "Notes and note pairs in Norgard's infinity series", J. of Mathematics and Music (2017). DOI: http://dx.doi.org/10.1080/17459737.2017.1299807

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Christopher Drexler-Lemire, Jeffrey Shallit, Notes and Note-Pairs in Noergaard's Infinity Series, arXiv:1402.3091 [math.CO], page 12f.
• Jørgen Mortensen, "Is Per Nørgård's infinity series unique?"

Crossrefs

Cf. A004718, A256184, A087808, A085144.

Programs

Haskell

a255723 n = a255723_list !! n
a255723_list = 0 : concat (transpose [map (subtract 2) a255723_list,
                                      map (-1 -) a255723_list,
                                      map (+ 2) a255723_list,
                                      tail a255723_list])