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A271832 Period 12 zigzag sequence: repeat [0,1,2,3,4,5,6,5,4,3,2,1]. 9
0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1 (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 (1,0,0,0,0,-1,1).

FORMULA

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

a(n) = a(n-1) - a(n-6) + a(n-7) for n>6.

a(n) = abs(n - 12*round(n/12)).

a(n) = Sum_{i=1..n} (-1)^floor((i-1)/6).

a(2n) = a(10n) = 2*A260686(n), a(2n+1) = A110551(n).

a(3n) = 3*A007877(n), a(4n) = a(8n) = 4*A011655(n).

a(6n) = A010677(n) = 6*A000035(n).

MAPLE

A271832:=n->[0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1][(n mod 12)+1]: seq(A271832(n), n=0..300);

MATHEMATICA

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

PROG

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

(PARI) lista(nn) = for(n=0, nn, print1(abs(n-12*round(n/12)), ", ")); \\ Altug Alkan, Apr 15 2016

CROSSREFS

Period k zigzag sequences: A000035 (k=2), A007877 (k=4), A260686 (k=6), A266313 (k=8), A271751 (k=10), this sequence (k=12), A279313 (k=14), A279319 (k=16), A158289 (k=18).

Cf. A010677, A011655, A110551.

Sequence in context: A245349 A122416 A134665 * A063260 A271859 A232240

Adjacent sequences:  A271829 A271830 A271831 * A271833 A271834 A271835

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Apr 15 2016

STATUS

approved

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Last modified October 21 14:57 EDT 2018. Contains 316424 sequences. (Running on oeis4.)