A271751 Period 10 zigzag sequence; repeat: [0, 1, 2, 3, 4, 5, 4, 3, 2, 1].

0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5

Offset: 0

Author

Wesley Ivan Hurt, Apr 13 2016

Keywords

• nonn
• easy

Comments

Decimal expansion of 11111/900009. - Elmo R. Oliveira, Mar 03 2024

Links

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

Crossrefs

Cf. A076839, A117444.

Period k zigzag sequences: A000035 (k=2), A007877 (k=4), A260686 (k=6), A266313 (k=8), this sequence (k=10), A271832 (k=12), A279313 (k=14), A279319 (k=16), A158289 (k=18).

Programs

Magma

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

Maple

a:=n->[0, 1, 2, 3, 4, 5, 4, 3, 2, 1][(n mod 10)+1]: seq(a(n), n=0..100);

Mathematica

CoefficientList[Series[x*(1 + x + x^2 + x^3 + x^4)/(1 - x + x^5 - x^6), {x, 0, 30}], x]

PARI

a(n) = abs(n-10*round(n/10)); \\ Altug Alkan, Apr 13 2016

Formula

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

a(n) = a(n-1) - a(n-5) + a(n-6) for n>5.

a(n) = abs(n - 10*round(n/10)).

a(n) = Sum_{i=1..n} (-1)^floor((i-1)/5).

a(2n) = 2*abs(A117444(n)).

a(2n+7) = 2*A076839(n)-1 for n>0.

a(n) = a(n-10) for n >= 10. - Wesley Ivan Hurt, Sep 07 2022