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 A042961 The sequence e when b is obtained by reversing the parity of Euler's partition function A000041. 2

%I

%S 1,0,1,0,2,0,2,0,3,1,3,1,4,2,4,3,6,4,8,5,10,7,13,8,16,11,19,15,23,18,

%T 29,25,34,30,43,38,54,46,64,58,79,68,93,86,112,105,133,127,160,156,

%U 187,188,228,226,270,269,320,323,381,379,450,456,531,538,625,637

%N The sequence e when b is obtained by reversing the parity of Euler's partition function A000041.

%C 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.

%C This produces 2 new sequences: d={i:c_i=1} and e=[ 1,e_1,... ] where C=1+Sum e_i*x^i.

%H Andrew Howroyd, <a href="/A042961/b042961.txt">Table of n, a(n) for n = 0..1000</a>

%o (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}

%o seq(n)={my(u=vector(n, i, 1-numbpart(i)%2), v=vector(n)); for(n=1, #v, v[n]=(u[n] + EulerT(v[1..n])[n])%2); concat([1], EulerT(v))} \\ _Andrew Howroyd_, May 04 2021

%Y Cf. A042951, A042960, A042962.

%K nonn

%O 0,5

%A _N. J. A. Sloane_ and _J. H. Conway_

%E Terms a(46) and beyond from _Andrew Howroyd_, May 04 2021

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Last modified September 19 16:34 EDT 2021. Contains 347564 sequences. (Running on oeis4.)