OFFSET
0,4
COMMENTS
A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion.
The version for ordered pairs is A080572.
FORMULA
a(n) = 2 * A080572(n - 2) + n.
EXAMPLE
The a(3) = 2 through a(8) = 15 pairs:
{1,3} {1,3} {1,3} {1,3} {1,3} {1,3}
{2,3} {2,3} {1,5} {1,5} {1,5} {1,5}
{2,3} {2,3} {1,7} {1,7}
{3,5} {2,6} {2,3} {2,3}
{4,5} {3,5} {2,6} {2,6}
{3,6} {2,7} {2,7}
{4,5} {3,5} {3,5}
{4,6} {3,6} {3,6}
{5,6} {3,7} {3,7}
{4,5} {4,5}
{4,6} {4,6}
{4,7} {4,7}
{5,6} {5,6}
{5,7} {5,7}
{6,7} {6,7}
MATHEMATICA
Table[Length[Select[Subsets[Range[n], {2}], Intersection[Position[Reverse[IntegerDigits[#[[1]], 2]], 1], Position[Reverse[IntegerDigits[#[[2]], 2]], 1]]!={}&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 28 2019
STATUS
approved