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A266313
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Period 8 zigzag sequence; repeat [0, 1, 2, 3, 4, 3, 2, 1].
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9
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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
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..85.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,-1,1).
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FORMULA
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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
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EXAMPLE
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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
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MAPLE
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A266313:=n->[0, 1, 2, 3, 4, 3, 2, 1][(n mod 8)+1]: seq(A266313(n), n=0..100);
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MATHEMATICA
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CoefficientList[Series[x*(1 + x + x^2 + x^3)/(1 - x + x^4 - x^5), {x, 0, 100}], x]
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PROG
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(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
(PARI) {a(n) = abs((n+4)\8*8-n)}; /* Michael Somos, Feb 27 2020 */
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Wesley Ivan Hurt, Dec 26 2015
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STATUS
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approved
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