A279313 Period 14 zigzag sequence: repeat [0,1,2,3,4,5,6,7,6,5,4,3,2,1].

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

Offset: 0

Author

Wesley Ivan Hurt, Dec 09 2016

Keywords

• nonn
• easy

Comments

Decimal expansion of 1111111/90000009. - Elmo R. Oliveira, Feb 21 2024

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,-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), this sequence (k=14), A279319 (k=16), A158289 (k=18).

Cf. A279316, A279321.

Programs

Magma

&cat[[0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1]: n in [0..10]];

Maple

A279313:=n->[0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1][(n mod 14)+1]: seq(A279313(n), n=0..200);

Mathematica

CoefficientList[Series[x*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)/(1 - x + x^7 - x^8), {x, 0, 100}], x]

PARI

a(n)=([0,1,0,0,0,0,0,0; 0,0,1,0,0,0,0,0; 0,0,0,1,0,0,0,0; 0,0,0,0,1,0,0,0; 0,0,0,0,0,1,0,0; 0,0,0,0,0,0,1,0; 0,0,0,0,0,0,0,1; 1,-1,0,0,0,0,0,1]^n*[0;1;2;3;4;5;6;7])[1,1] \\ Charles R Greathouse IV, Dec 12 2016

Formula

G.f.: x*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)/(1 - x + x^7 - x^8).

a(n) = a(n-1) - a(n-7) + a(n-8) for n > 7.

a(n) = abs(n - 14*round(n/14)).

a(n) = Sum_{i=1..n} (-1)^floor((i-1)/7).

a(2n) = 2*A279316(n), a(2n+1) = A279321(n).

a(n) = a(n-14) for n >= 14. - Wesley Ivan Hurt, Sep 07 2022