A256185 Second of two variations by Per Nørgård of his "infinity sequence", cf. A004718: v(0) = 0; v(3*n) = -v(n); v(3*n+1) = v(n) - 3; v(3*n+2) = -2 - v(n).

0, -3, -2, 3, -6, 1, 2, -5, 0, -3, 0, -5, 6, -9, 4, -1, -2, -3, -2, -1, -4, 5, -8, 3, 0, -3, -2, 3, -6, 1, 0, -3, -2, 5, -8, 3, -6, 3, -8, 9, -12, 7, -4, 1, -6, 1, -4, -1, 2, -5, 0, 3, -6, 1, 2, -5, 0, 1, -4, -1, 4, -7, 2, -5, 2, -7, 8, -11, 6, -3, 0, -5, 0

Offset: 0

Author

Reinhard Zumkeller, Mar 19 2015

Keywords

• sign

Comments

Per Nørgård's surname is also written as Noergaard;

for all odd j exists k such that abs(a(k+1)-a(k)) = j, in contrast to A004718, where this holds also for even j > 0, see link.

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 13

Crossrefs

Cf. A004718, A256184, A087808, A085144, A255723.

Programs

Haskell

a256185 n = a256185_list !! n
a256185_list = 0 : concat (transpose [map (subtract 3) a256185_list,
                                      map (-2 -) a256185_list,
                                      map negate $ tail a256185_list])