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Search: id:A083904
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| A083904 |
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G.f. 1/(1-x) * sum(k>=0, 3^k*x^2^(k+1)/(1+x^2^k)). |
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+0
1
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| 0, 1, 0, 4, 3, 1, 0, 13, 12, 10, 9, 4, 3, 1, 0, 40, 39, 37, 36, 31, 30, 28, 27, 13, 12, 10, 9, 4, 3, 1, 0, 121, 120, 118, 117, 112, 111, 109, 108, 94, 93, 91, 90, 85, 84, 82, 81, 40, 39, 37, 36, 31, 30, 28, 27, 13, 12, 10, 9, 4, 3, 1, 0, 364, 363, 361, 360
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Distance to next number of form 2^k-1, written down in binary, then interpreted as ternary. Thus the numbers have no 2 in ternary representation.
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LINKS
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R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
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a(1)=0, a(2n) = 3a(n)+1, a(2n+1) = 3a(n).
a(n) = 1/2*(3^(floor(log2(n))+1)-1) - A005836(n).
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PROGRAM
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(PARI) for(n=1, 100, l=ceil(log(n)/log(2)):t=polcoeff(1/(1-x)*sum(k=0, l, 3^k*(x^2^(k+1))/(1+x^2^k)), n):print1(t", "))
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CROSSREFS
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Cf. A005823, A005836.
Adjacent sequences: A083901 A083902 A083903 this_sequence A083905 A083906 A083907
Sequence in context: A021236 A136590 A117026 this_sequence A129810 A016500 A046546
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KEYWORD
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nonn,easy
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), Jun 18 2003
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