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A050602
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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))
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7
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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, 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, 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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,12
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COMMENTS
| Comment from N. J. A. Sloane, Jun 21 2011: Apparently the same as the following sequence. Infinite square array read by antidiagonals, where T(m,n) = length of longest carry propagation when u and v are added in binary, for u >= 0, v >= 0.
The array begins:
0 0 0 0 0 0 0 0 ...
0 1 0 2 0 1 0 3 ...
0 0 1 1 0 0 2 2 ...
0 2 1 1 0 3 2 2 ...
0 0 0 0 1 1 1 1 ...
0 1 0 3 1 1 1 2 ...
0 0 2 2 1 1 1 1 ...
0 3 2 2 1 2 1 1 ...
...
See A192054 for definition of carry propagation. For example, T(3,5) = 3, since adding 011 + 101 in binary, the initial 1 propagates three places.
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REFERENCES
| N. Pippenger, Analysis of carry propagation in addition: an elementary approach, J. Algorithms, 42 (2002), 317-333.
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FORMULA
| a(n) -> add3c( (n-((trinv(n)*(trinv(n)-1))/2)), (((trinv(n)-1)*(((1/2)*trinv(n))+1))-n) )
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MAPLE
| 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;
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CROSSREFS
| Row/Column 1: A007814, Row/Column 2: A050605, Row/Column 3: A050606.
Cf. A050600, A050601, A003056, A048720 (for the Maple implementation of trinv and XORnos, ANDnos).
Cf. also A192054.
Sequence in context: A079548 A175620 A079071 * A065040 A057595 A035201
Adjacent sequences: A050599 A050600 A050601 * A050603 A050604 A050605
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KEYWORD
| nonn,tabl,nice
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AUTHOR
| Antti Karttunen Jun 22 1999
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