A256184 First of two variations by Per Nørgård of his "infinity sequence", cf. A004718: u(0) = 0; u(3*n) = -u(n); u(3*n+1) = u(n) - 2; u(3*n+2) = u(n) - 1.

0, -2, -1, 2, -4, -3, 1, -3, -2, -2, 0, 1, 4, -6, -5, 3, -5, -4, -1, -1, 0, 3, -5, -4, 2, -4, -3, 2, -4, -3, 0, -2, -1, -1, -1, 0, -4, 2, 3, 6, -8, -7, 5, -7, -6, -3, 1, 2, 5, -7, -6, 4, -6, -5, 1, -3, -2, 1, -3, -2, 0, -2, -1, -3, 1, 2, 5, -7, -6, 4, -6, -5

Offset: 0

Author

Reinhard Zumkeller, Mar 19 2015

Keywords

• sign

Comments

Per Nørgård's surname is also written as Noergaard.

Not squarefree in contrast to A004718, first repetition of order 3: a(32) = a(33) = a(34) = -1, see link.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• 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).
• Christopher Drexler-Lemire and Jeffrey Shallit, Notes and Note-Pairs in Noergaard's Infinity Series, arXiv:1402.3091 [math.CO], 2014, page 13.

Crossrefs

Cf. A004718, A256185, A087808, A085144, A255723.

Programs

Haskell

a256184 n = a256184_list !! n
a256184_list = 0 : concat (transpose [map (subtract 2) a256184_list,
                                      map (subtract 1) a256184_list,
                                      map negate $ tail a256184_list])

Python

from functools import lru_cache
@lru_cache(maxsize=None)
def a(n): return 0 if n == 0 else (a(n//3) - (3-n%3)) if n%3 else -a(n//3)
print([a(n) for n in range(72)]) # Michael S. Branicky, Sep 02 2021