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A131531
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Period 6: repeat [0, 0, 1, 0, 0, -1].
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18
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0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0
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OFFSET
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1,1
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COMMENTS
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The square array of this sequence in the top row and further rows defined as first differences of preceding rows starts (see A167613):
. 0, 0, 1, 0, 0, -1, ...
. 0, 1, -1, 0, -1, 1, ... = A092220,
. 1, -2, 1, -1, 2, -1, ... = A131556,
. -3, 3, -2, 3, -3 2, ...
. 6, -5, 5, -6, 5, -5, ...
. -11, 10, -11, 11, -10, 11, ...
. 21, -21, 22, -21, 21, -22, ...
. -42, 43, -43, 42, -43, 43, ...
The main diagonal in this array is A001045; the first superdiagonal is the negated elements of A001045, the second superdiagonal is A078008.
The left column of the array is basically the inverse binomial transform, (-1)^n * A024495(n), assuming offset 0.
The second column of the array is A131708 with alternating signs, and the third column is A024493 with alternating signs (both assuming offset 0). (End)
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LINKS
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FORMULA
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a(n) = -cos(Pi*(n-1)/3)/3 + sin(Pi*(n-1)/3)/sqrt(3) - (-1)^n/3. - R. J. Mathar, Oct 08 2011
a(n) = ( (-1)^n - (-1)^floor((n+2)/3) )/2. - Bruno Berselli, Jul 09 2013
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MAPLE
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MATHEMATICA
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PadRight[{}, 120, {0, 0, 1, 0, 0, -1}] (* Harvey P. Dale, Nov 11 2012 *)
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PROG
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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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EXTENSIONS
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STATUS
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approved
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