A266313 Period 8 zigzag sequence; repeat [0, 1, 2, 3, 4, 3, 2, 1].

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

Offset: 0

Author

Wesley Ivan Hurt, Dec 26 2015

Keywords

• nonn
• easy

Comments

Decimal expansion of 1111/90009. - Elmo R. Oliveira, Mar 03 2024

Examples

			G.f. = x + 2*x^2 + 3*x^3 + 4*x^4 + 3*x^5 + 2*x^6 + x^7 + x^9 + ... - _Michael Somos_, Feb 27 2020
		

Links

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

Crossrefs

Period k zigzag sequences: A000035 (k=2), A007877 (k=4), A260686 (k=6), this sequence (k=8), A271751 (k=10), A271832 (k=12), A279313 (k=14), A279319 (k=16), A158289 (k=18).

Cf. A084101.

Programs

Magma

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

Maple

A266313:=n->[0, 1, 2, 3, 4, 3, 2, 1][(n mod 8)+1]: seq(A266313(n), n=0..100);

Mathematica

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

PARI

x='x+O('x^100); concat(0, Vec(x*(1+x+x^2+x^3)/(1-x+x^4-x^5))) \\ Altug Alkan, Dec 29 2015

PARI

{a(n) = abs((n+4)\8*8-n)}; /* Michael Somos, Feb 27 2020 */

Formula

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

a(n) = a(n-1) - a(n-4) + a(n-5) for n > 4.

a(n) = Sum_{i = 1..n} (-1)^floor((i-1)/4).

a(2n) = 2*A007877(n); a(2n+1) = A084101(n).

a(n) = abs(n - 8*round(n/8)). - Jon E. Schoenfield, Jan 01 2016

Euler transform of length 8 sequence [2, 0, 0, -2, 0, 0, 0, 1]. - Michael Somos, Feb 27 2020

a(n) = a(n-8) for n >= 8. - Wesley Ivan Hurt, Sep 07 2022