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A011765
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Period 4: repeat [0, 0, 0, 1].
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11
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0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1
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OFFSET
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1,1
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COMMENTS
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Arises in connection with leap years, years of U.S. Presidential elections, Olympic Games, etc.
Note that leap years define a sequence with period length 400, unlike A121262 which has period length 4. - R. J. Mathar, Dec 19 2008
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LINKS
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FORMULA
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a(n) = (1+(-1)^n)*(1+i^n)/4 with i=sqrt(-1). - Bruno Berselli, Mar 14 2011
a(n) = 1/4 - sin(Pi*(n-1)/2)/2 + (-1)^n/4. - R. J. Mathar, Oct 08 2011
The characteristic function of numbers that are multiples of 4. For the general case: the characteristic function of numbers that are multiples of m is a(n) = floor(n/m) - floor((n-1)/m), m,n > 0. - Boris Putievskiy, May 08 2013
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MAPLE
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MATHEMATICA
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PadRight[{}, 120, {0, 0, 0, 1}] (* or *) LinearRecurrence[{0, 0, 0, 1}, {0, 0, 0, 1}, 120] (* Harvey P. Dale, Aug 20 2012 *)
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PROG
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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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