Search: id:A050600
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%I A050600
%S A050600 0,1,0,1,2,0,1,1,1,0,1,3,2,3,0,1,1,2,2,1,0,1,2,1,2,1,2,0,1,1,1,1,1,1,1,
               0,1,4,3,4,
%T A050600 2,4,3,4,0,1,1,3,3,2,2,3,3,1,0,1,2,1,3,2,2,2,3,1,2,0,1,1,1,1,2,2,2,2,1,
               1,1,0,1,3,
%U A050600 2,3,1,3,2,3,1,3,2,3,0,1,1,2,2,1,1,2,2,1,1,2,2,1,0,1,2,1,2,1,2,1,2,1,2,
               1,2,1,2,0
%N A050600 Recursion counts for summation table A003056 with formula a(y,0) = y, 
               a(y,x) = a((y XOR x),2*(y AND x))
%C A050600 Count the summation table A003056 with recursive formula based on identity 
               A+B = (A XOR B)+ 2*(A AND B) given by Schroeppel and then this table 
               gives the number of recursion steps to get the final result.
%H A050600 Beeler, M., Gosper, R. W. and Schroeppel, R., <a href="http://www.inwap.com/
               pdp10/hbaker/hakmem/boolean.html#item23">HAKMEM, ITEM 23 (Schroeppel)</
               a>
%F A050600 a(n) -> add1c( (n-((trinv(n)*(trinv(n)-1))/2)), (((trinv(n)-1)*(((1/2)*trinv(n))+1))-n) 
               )
%p A050600 add1c := proc(a,b) option remember; if(0 = b) then RETURN(0); else RETURN(1+add_c(XORnos(a,
               b),2*ANDnos(a,b))); fi; end;
%Y A050600 Column 1: A001511, column 2: A050603, column 3: A050604.
%Y A050600 Cf. A050601, A050602, A003056, A048720 (for the Maple implementation 
               of trinv and XORnos, ANDnos)
%Y A050600 Sequence in context: A105553 A117165 A024363 this_sequence A129691 A117454 
               A115357
%Y A050600 Adjacent sequences: A050597 A050598 A050599 this_sequence A050601 A050602 
               A050603
%K A050600 nonn,tabl
%O A050600 0,5
%A A050600 Antti Karttunen Jun 22 1999

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