login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A041003 The sequence e, given that c is a left shift by one place of b. 4
1, 1, 1, 2, 3, 3, 4, 6, 7, 8, 10, 12, 14, 16, 20, 23, 26, 30, 36, 41, 47, 55, 64, 73, 83, 96, 111, 125, 144, 165, 187, 211, 241, 272, 306, 346, 391, 439, 493, 553, 622, 695, 779, 871, 974, 1086, 1211, 1348, 1502, 1671, 1857, 2061, 2288, 2533, 2808, 3107, 3439, 3800, 4199, 4634, 5113 (list; graph; refs; listen; history; text; internal format)
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

Cf. A041002, A041004.

Sequence in context: A265109 A301277 A029033 * A067592 A101195 A036018

Adjacent sequences:  A041000 A041001 A041002 * A041004 A041005 A041006

KEYWORD

nonn,easy,eigen

AUTHOR

N. J. A. Sloane

EXTENSIONS

Terms a(50) and beyond from Andrew Howroyd, Apr 14 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 09:14 EDT 2021. Contains 343995 sequences. (Running on oeis4.)