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 A041004 The sequence b, given that c is a left shift by one place of b. 3
 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Map a binary sequence b=[ b_1,... ] to a binary sequence c=[ c_1,... ] so that C=1/Product (1-x^i)^c_i == 1+Sum b_i*x^i mod 2. This produces 2 new sequences: d={i:c_i=1} and e=[ 1,e_1,... ] where C=1+Sum e_i*x^i. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1000 FORMULA From Andrew Howroyd, Apr 15 2021: (Start) a(n) = A041003(n+1) mod 2. G.f.: A(x) = 1 + Sum_{k>=0} x^A041002(k). (End) PROG (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)} seq(n)={my(v=vector(n+1)); v[1]=1; for(n=2, #v, v[n]=(v[n-1] + EulerT(v[2..n])[n-1])%2); v} \\ Andrew Howroyd, Apr 14 2021 CROSSREFS Cf. A041002, A041003. Sequence in context: A217206 A189097 A189094 * A141736 A190188 A278513 Adjacent sequences: A041001 A041002 A041003 * A041005 A041006 A041007 KEYWORD nonn,easy,eigen AUTHOR N. J. A. Sloane EXTENSIONS Terms a(53) and beyond from Andrew Howroyd, Apr 14 2021 STATUS approved

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Last modified September 23 09:19 EDT 2023. Contains 365544 sequences. (Running on oeis4.)