OFFSET
0,4
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)
Euler transform of A041004.
G.f.: A(x) = 1/Product_{k>=1} (1 - x^k)^(a(k+1) mod 2). (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); concat([1], EulerT(v[2..n+1]))} \\ Andrew Howroyd, Apr 14 2021
CROSSREFS
KEYWORD
nonn,easy,eigen
AUTHOR
EXTENSIONS
Terms a(50) and beyond from Andrew Howroyd, Apr 14 2021
STATUS
approved