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A253513
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The characteristic function of the multiples of eight.
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4
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1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,1
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COMMENTS
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Period 8: repeat [1, 0, 0, 0, 0, 0, 0, 0].
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LINKS
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FORMULA
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a(n) = floor(n/8) - floor((n-1)/8).
a(n) = sin((sin(Pi*(n+1)/2)^2)*Pi*(n+2)/4)/2 + (sin(Pi*(n+1)/2)^2)/4 + sin(Pi*(n+1)/2)/4.
G.f.: 1/(1-x^8). (End)
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0}, 120] (* or *) PadRight[ {}, 120, {1, 0, 0, 0, 0, 0, 0, 0}] (* Harvey P. Dale, Apr 07 2017 *)
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PROG
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(Python)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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