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A010751
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Up 1, down 2, up 3, down 4, ...
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0
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0, 1, 0, -1, 0, 1, 2, 1, 0, -1, -2, -1, 0, 1, 2, 3, 2, 1, 0, -1, -2, -3, -2, -1, 0, 1, 2, 3, 4, 3, 2, 1, 0, -1, -2, -3, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -5, -4
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OFFSET
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0,7
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LINKS
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Table of n, a(n) for n=0..80.
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FORMULA
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a(n)=x+1-(sign(x(2x+1)-y(2y+1)))*(n-2x^2-3x-1) where x=floor((-1-sqrt(1+8n))/4), y=-floor((1-sqrt(1+8n))/4), sign(x)=abs(x)/x when x is not 0 and sign(0)=0, floor(x)=the greatest integer less than or equal to x, sqrt(x)=the principal square root of x and abs(x)=the absolute value (or magnitude) of x. - Mark Spindler, Mar 25 2004
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MATHEMATICA
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n=(the index); x = -1; y = 0; While[n != 0, While[y != x && n != 0, y--; n-- ]; While[y != -x && n != 0, n--; y++ ]; x-- ]; Print[ -y] provided by Gregory Puleo n = (the index); a = Floor[(-1 - Sqrt[1 + 8* n])/4]; b = -Floor[(1 - Sqrt[1 + 8*n])/4]; a + 1 - Sign[a*(2*a + 1) - b*(2*b + 1)]*(n - 2*a^2 - 3*a - 1) (provided by Mark Spindler)
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CROSSREFS
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Sequence in context: A054848 A194525 A065368 * A194523 A180714 A170959
Adjacent sequences: A010748 A010749 A010750 * A010752 A010753 A010754
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KEYWORD
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sign
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AUTHOR
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David Berends (dave(AT)pgt.com)
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STATUS
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approved
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