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A266313 Period 8 zigzag sequence; repeat [0, 1, 2, 3, 4, 3, 2, 1]. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..85.

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

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

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]

PROG

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

(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

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.

Sequence in context: A017889 A017879 A179764 * A017869 A107469 A167600

Adjacent sequences:  A266310 A266311 A266312 * A266314 A266315 A266316

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Dec 26 2015

STATUS

approved

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Last modified February 21 22:56 EST 2018. Contains 299427 sequences. (Running on oeis4.)