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A325102
Number of ordered pairs of positive integers up to n with no binary carries.
7
0, 0, 2, 2, 8, 10, 12, 12, 26, 32, 38, 40, 46, 48, 50, 50, 80, 94, 108, 114, 128, 134, 140, 142, 156, 162, 168, 170, 176, 178, 180, 180, 242, 272, 302, 316, 346, 360, 374, 380, 410, 424, 438, 444, 458, 464, 470, 472, 502, 516, 530, 536, 550, 556, 562, 564, 578
OFFSET
0,3
COMMENTS
A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion.
FORMULA
a(n) = 2 * A325103(n).
EXAMPLE
The a(2) = 2 through a(6) = 12 pairs:
(1,2) (1,2) (1,2) (1,2) (1,2) (1,2)
(2,1) (2,1) (1,4) (1,4) (1,4) (1,4)
(2,1) (2,1) (1,6) (1,6)
(2,4) (2,4) (2,1) (2,1)
(3,4) (2,5) (2,4) (2,4)
(4,1) (3,4) (2,5) (2,5)
(4,2) (4,1) (3,4) (3,4)
(4,3) (4,2) (4,1) (4,1)
(4,3) (4,2) (4,2)
(5,2) (4,3) (4,3)
(5,2) (5,2)
(6,1) (6,1)
MATHEMATICA
Table[Length[Select[Tuples[Range[n], 2], Intersection[Position[Reverse[IntegerDigits[#[[1]], 2]], 1], Position[Reverse[IntegerDigits[#[[2]], 2]], 1]]=={}&]], {n, 0, 30}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 28 2019
STATUS
approved