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A083905
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G.f.: 1/(1-x) * sum(k>=0, (-1)^k*x^2^(k+1)/(1+x^2^k)).
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2
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0, 1, 0, 0, -1, 1, 0, 1, 0, 2, 1, 0, -1, 1, 0, 0, -1, 1, 0, -1, -2, 0, -1, 1, 0, 2, 1, 0, -1, 1, 0, 1, 0, 2, 1, 0, -1, 1, 0, 2, 1, 3, 2, 1, 0, 2, 1, 0, -1, 1, 0, -1, -2, 0, -1, 1, 0, 2, 1, 0, -1, 1, 0, 0, -1, 1, 0, -1, -2, 0, -1, 1, 0, 2, 1, 0, -1, 1, 0, -1, -2, 0, -1, -2, -3, -1
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OFFSET
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1,10
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COMMENTS
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For all n, a(3*A006288(n)) = 0 as proved in Russian forum dxdy.ru - see link.
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LINKS
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FORMULA
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a(1)=0, a(2n) = -a(n)+1, a(2n+1) = -a(n).
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PROG
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(PARI) for(n=1, 100, l=ceil(log(n)/log(2)); t=polcoeff(1/(1-x)*sum(k=0, l, (-1)^k*(x^2^(k+1))/(1+x^2^k)) + O(x^(n+1)), n); print1(t", "))
(PARI) a(n) = sum(i=0, logint(n, 2)-1, if(!bittest(n, i), (-1)^i)); \\ Kevin Ryde, May 24 2021
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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