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A325103
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Number of increasing pairs of positive integers up to n with no binary carries.
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17
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0, 0, 1, 1, 4, 5, 6, 6, 13, 16, 19, 20, 23, 24, 25, 25, 40, 47, 54, 57, 64, 67, 70, 71, 78, 81, 84, 85, 88, 89, 90, 90, 121, 136, 151, 158, 173, 180, 187, 190, 205, 212, 219, 222, 229, 232, 235, 236, 251, 258, 265, 268, 275, 278, 281, 282, 289, 292, 295, 296
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OFFSET
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0,5
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COMMENTS
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A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion.
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LINKS
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FORMULA
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EXAMPLE
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The a(2) = 1 through a(9) = 16 pairs:
{1,2} {1,2} {1,2} {1,2} {1,2} {1,2} {1,2} {1,2}
{1,4} {1,4} {1,4} {1,4} {1,4} {1,4}
{2,4} {2,4} {1,6} {1,6} {1,6} {1,6}
{3,4} {2,5} {2,4} {2,4} {1,8} {1,8}
{3,4} {2,5} {2,5} {2,4} {2,4}
{3,4} {3,4} {2,5} {2,5}
{2,8} {2,8}
{3,4} {2,9}
{3,8} {3,4}
{4,8} {3,8}
{5,8} {4,8}
{6,8} {4,9}
{7,8} {5,8}
{6,8}
{6,9}
{7,8}
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MATHEMATICA
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Table[Length[Select[Subsets[Range[n], {2}], Intersection[Position[Reverse[IntegerDigits[#[[1]], 2]], 1], Position[Reverse[IntegerDigits[#[[2]], 2]], 1]]=={}&]], {n, 0, 30}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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