cp's OEIS Frontend

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

%I A325104 #6 Jul 27 2019 14:57:51
%S A325104 0,0,0,2,2,5,9,15,15,20,26,35,43,54,66,80,80,89,99,114,126,143,161,
%T A325104 182,198,219,241,266,290,317,345,375,375,392,410,437,457,486,516,551,
%U A325104 575,608,642,681,717,758,800,845,877,918,960,1007,1051,1100,1150,1203
%N A325104 Number of increasing pairs of positive integers up to n with at least one binary carry.
%C A325104 A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion.
%C A325104 The version for ordered pairs is A080572.
%F A325104 a(n) = 2 * A080572(n - 2) + n.
%e A325104 The a(3) = 2 through a(8) = 15 pairs:
%e A325104   {1,3}  {1,3}  {1,3}  {1,3}  {1,3}  {1,3}
%e A325104   {2,3}  {2,3}  {1,5}  {1,5}  {1,5}  {1,5}
%e A325104                 {2,3}  {2,3}  {1,7}  {1,7}
%e A325104                 {3,5}  {2,6}  {2,3}  {2,3}
%e A325104                 {4,5}  {3,5}  {2,6}  {2,6}
%e A325104                        {3,6}  {2,7}  {2,7}
%e A325104                        {4,5}  {3,5}  {3,5}
%e A325104                        {4,6}  {3,6}  {3,6}
%e A325104                        {5,6}  {3,7}  {3,7}
%e A325104                               {4,5}  {4,5}
%e A325104                               {4,6}  {4,6}
%e A325104                               {4,7}  {4,7}
%e A325104                               {5,6}  {5,6}
%e A325104                               {5,7}  {5,7}
%e A325104                               {6,7}  {6,7}
%t A325104 Table[Length[Select[Subsets[Range[n],{2}],Intersection[Position[Reverse[IntegerDigits[#[[1]],2]],1],Position[Reverse[IntegerDigits[#[[2]],2]],1]]!={}&]],{n,0,30}]
%Y A325104 Cf. A006218, A050315, A080572, A247935, A267610, A267700.
%Y A325104 Cf. A325094, A325096, A325098, A325102, A325103, A325106, A325108, A325123.
%K A325104 nonn
%O A325104 0,4
%A A325104 _Gus Wiseman_, Mar 28 2019