%I A050602
%S A050602 0,0,0,0,1,0,0,0,0,0,0,2,1,2,0,0,0,1,1,0,0,0,1,0,1,0,1,0,0,0,0,0,0,0,0,
               0,0,3,2,3,
%T A050602 1,3,2,3,0,0,0,2,2,1,1,2,2,0,0,0,1,0,2,1,1,1,2,0,1,0,0,0,0,0,1,1,1,1,0,
               0,0,0,0,2,
%U A050602 1,2,0,2,1,2,0,2,1,2,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,
               0,1,0,1,0
%N A050602 Recursion counts for summation table A003056 with formula a(y,x): if 
               (y AND x) = 0 then (y XOR x), otherwise = a((y XOR x),2*(y AND x))
%F A050602 a(n) -> add3c( (n-((trinv(n)*(trinv(n)-1))/2)), (((trinv(n)-1)*(((1/2)*trinv(n))+1))-n) 
               )
%p A050602 add3c := proc(a,b) option remember; if(0 = ANDnos(a,b)) then RETURN(0); 
               else RETURN(1+add3c(XORnos(a,b),2*ANDnos(a,b))); fi; end;
%Y A050602 Row/Column 1: A007814, Row/Column 2: A050605, Row/Column 3: A050606.
%Y A050602 Cf. A050600, A050601, A003056, A048720 (for the Maple implementation 
               of trinv and XORnos, ANDnos)
%Y A050602 Sequence in context: A070965 A079548 A079071 this_sequence A065040 A057595 
               A035201
%Y A050602 Adjacent sequences: A050599 A050600 A050601 this_sequence A050603 A050604 
               A050605
%K A050602 nonn,tabl
%O A050602 0,12
%A A050602 Antti Karttunen Jun 22 1999