A325104 Number of increasing pairs of positive integers up to n with at least one binary carry.

0, 0, 0, 2, 2, 5, 9, 15, 15, 20, 26, 35, 43, 54, 66, 80, 80, 89, 99, 114, 126, 143, 161, 182, 198, 219, 241, 266, 290, 317, 345, 375, 375, 392, 410, 437, 457, 486, 516, 551, 575, 608, 642, 681, 717, 758, 800, 845, 877, 918, 960, 1007, 1051, 1100, 1150, 1203

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.

Links

Table of n, a(n) for n=0..55.

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

Cf. A006218, A050315, A080572, A247935, A267610, A267700.

Cf. A325094, A325096, A325098, A325102, A325103, A325106, A325108, A325123.

Sequence in context: A131133 A096569 A076607 * A054229 A212812 A214727

Adjacent sequences: A325101 A325102 A325103 * A325105 A325106 A325107

Keyword

nonn

Author

Gus Wiseman, Mar 28 2019

Status

approved