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A131734
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Hexaperiodic [0, 1, 0, 1, 0, -1].
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1
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0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: x*(1+x^2-x^4)/(1-x^6).
Recurrence: a(n) = a(n-6).
a(n) = (1-(-1)^n)*(-1)^floor(2n/3)/2.
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EXAMPLE
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G.f. = x + x^3 - x^5 + x^7 + x^9 - x^11 + x^13 + x^15 - x^17 + x^19 + x^21 + ...
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MAPLE
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MATHEMATICA
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CoefficientList[Series[x (1 + x^2 - x^4)/(1 - x^6), {x, 0, 100}], x] (* Wesley Ivan Hurt, Apr 06 2015 *)
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PROG
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(Magma) [(1-(-1)^n)*(-1)^Floor(2*n/3)/2 : n in [0..100]]; // Wesley Ivan Hurt, Apr 06 2015
(PARI) {a(n) = [ 0, 1, 0, 1, 0, -1, 0, 1][n%6 + 1]}; /* Michael Somos, Nov 11 2015 */
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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