A279319 Period 16 zigzag sequence: repeat [0,1,2,3,4,5,6,7,8,7,6,5,4,3,2,1].

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

Offset: 0

Author

Wesley Ivan Hurt, Dec 09 2016

Keywords

• nonn
• easy

Comments

Decimal expansion of 11111111/900000009. - Elmo R. Oliveira, Feb 20 2024

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,-1,1).

Crossrefs

Period k zigzag sequences: A000035 (k=2), A007877 (k=4), A260686 (k=6), A266313 (k=8), A271751 (k=10), A271832 (k=12), A279313 (k=14), this sequence (k=16), A158289 (k=18).

Programs

Magma

&cat[[0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1]: n in [0..5]];

Mathematica

PadRight[{}, 120, {0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1}] (* Vincenzo Librandi, Dec 10 2016 *)
With[{k = 16}, Table[Min[Abs[# - k], #] &@ Mod[n, k], {n, 0, 120}]] (* or *)
CoefficientList[Series[x (1 + x) (1 + x^2) (1 + x^4)/((1 - x) (1 + x^8)), {x, 0, 120}], x] (* Michael De Vlieger, Dec 10 2016 *)

Python

def A279319(n): return (0,1,2,3,4,5,6,7,8,7,6,5,4,3,2,1)[n&15] # Chai Wah Wu, Mar 02 2023

Formula

a(n) = abs(n - 16*round(n/16)).

G.f.: x*(1 + x)*(1 + x^2)*(1 + x^4)/((1 - x)*(1 + x^8)). - Ilya Gutkovskiy, Dec 10 2016

a(n) = a(n-1)-a(n-8)+a(n-9). - Wesley Ivan Hurt, Nov 18 2021

a(n) = a(n-16) for n >= 16. - Wesley Ivan Hurt, Sep 07 2022