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 A325104 Number of increasing pairs of positive integers up to n with at least one binary carry. 16
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified February 27 15:39 EST 2020. Contains 332307 sequences. (Running on oeis4.)