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A042961 The sequence e when b is obtained by reversing the parity of Euler's partition function A000041. 2
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, 29, 25, 34, 30, 43, 38, 54, 46, 64, 58, 79, 68, 93, 86, 112, 105, 133, 127, 160, 156, 187, 188, 228, 226, 270, 269, 320, 323, 381, 379, 450, 456, 531, 538, 625, 637 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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

PROG

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

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

CROSSREFS

Cf. A042951, A042960, A042962.

Sequence in context: A302643 A319973 A025804 * A029190 A166865 A300575

Adjacent sequences:  A042958 A042959 A042960 * A042962 A042963 A042964

KEYWORD

nonn

AUTHOR

N. J. A. Sloane and J. H. Conway

EXTENSIONS

Terms a(46) and beyond from Andrew Howroyd, May 04 2021

STATUS

approved

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Last modified August 2 05:02 EDT 2021. Contains 346409 sequences. (Running on oeis4.)