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A271751 Period 10 zigzag sequence; repeat: [0, 1, 2, 3, 4, 5, 4, 3, 2, 1]. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Decimal expansion of 11111/900009. - Elmo R. Oliveira, Mar 03 2024
LINKS
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
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]
PROG
(Magma) &cat[[0, 1, 2, 3, 4, 5, 4, 3, 2, 1]: n in [0..10]];
(PARI) a(n) = abs(n-10*round(n/10)); \\ Altug Alkan, Apr 13 2016
CROSSREFS
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).
Sequence in context: A237985 A143055 A339388 * A017890 A134011 A280913
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Apr 13 2016
STATUS
approved

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Last modified June 21 07:08 EDT 2024. Contains 373540 sequences. (Running on oeis4.)