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Search: id:A050600
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| A050600 |
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Recursion counts for summation table A003056 with formula a(y,0) = y, a(y,x) = a((y XOR x),2*(y AND x)) |
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+0
8
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| 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, 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, 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
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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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.
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LINKS
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Beeler, M., Gosper, R. W. and Schroeppel, R., HAKMEM, ITEM 23 (Schroeppel)
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FORMULA
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a(n) -> add1c( (n-((trinv(n)*(trinv(n)-1))/2)), (((trinv(n)-1)*(((1/2)*trinv(n))+1))-n) )
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MAPLE
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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;
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CROSSREFS
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Column 1: A001511, column 2: A050603, column 3: A050604.
Cf. A050601, A050602, A003056, A048720 (for the Maple implementation of trinv and XORnos, ANDnos)
Sequence in context: A105553 A117165 A024363 this_sequence A129691 A117454 A115357
Adjacent sequences: A050597 A050598 A050599 this_sequence A050601 A050602 A050603
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KEYWORD
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nonn,tabl
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AUTHOR
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Antti Karttunen Jun 22 1999
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