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Search: id:A049773
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| A049773 |
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Triangular array T read by rows: if row n is r(1),...,r(m), then row n+1 is 2r(1)-1,...,2r(m)-1,2r(1),...,2r(m). |
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+0
6
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| 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 7, 2, 6, 4, 8, 1, 9, 5, 13, 3, 11, 7, 15, 2, 10, 6, 14, 4, 12, 8, 16, 1, 17, 9, 25, 5, 21, 13, 29, 3, 19, 11, 27, 7, 23, 15, 31, 2, 18, 10, 26, 6, 22, 14, 30, 4, 20, 12, 28, 8, 24, 16, 32, 1, 33, 17, 49, 9, 41, 25, 57, 5, 37, 21, 53, 13, 45, 29, 61, 3, 35, 19
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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n-th row = (r(1),r(2),...,r(m)), where m=2^(n-1), satisfies r(r(k))=k for k=1,2,...,m and has exactly 2^[ n/2 ] solutions of r(k)=k. (The function r(k) reverses bits. Or rather, r(k)=revbits(k-1)+1.)
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EXAMPLE
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Rows: {1}; {1,2}; {1,3,2,4}; {1,5,3,7,2,6,4,8}; ...
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PROGRAM
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(PARI) a(n, k)= if(k<=0|k >= n, 0, if(k%2, n\2)+a(n\2, k\2)); T(n, k)= if(k<=0|k>2^n/2, 0, 1+a(2^n/2, k-1)) - Michael Somos
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CROSSREFS
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Sum of odd-indexed terms of n-th row gives A007582. Sum of even-indexed terms gives A049775.
A030109 is another version.
Sequence in context: A094193 A108712 A003602 this_sequence A123021 A028914 A106466
Adjacent sequences: A049770 A049771 A049772 this_sequence A049774 A049775 A049776
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KEYWORD
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nonn,tabf,nice
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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