A105234 Central column of a Moebius-binomial triangle.

1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1

Offset

0,1

Comments

Central column of A105586.

Partial sums are A105235.

The characteristic function of the numbers that are not even squarefree numbers (i.e., not in A039956). - Amiram Eldar, Dec 09 2025

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for characteristic functions.

Formula

a(n) = binomial(abs(mu(2n)), abs(mu(n))).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 - 2/Pi^2. - Amiram Eldar, Dec 09 2025

Mathematica

a[n_]:=Binomial[Abs[MoebiusMu[2n]], Abs[MoebiusMu[n]]]; Table[a[n], {n, 0, 100}] (* James C. McMahon, Jan 22 2024 *)

Prog

(PARI) A105234(n) = if(n<2, 1, binomial(abs(moebius(2*n)), abs(moebius(n)))); \\ Antti Karttunen, Sep 13 2017

Crossrefs

Cf. A008683, A039956, A105235, A105586, A105597.

Sequence in context: A152822 A118831 A118828 * A285599 A284386 A286922

Adjacent sequences: A105231 A105232 A105233 * A105235 A105236 A105237

Keyword

easy,nonn

Author

Paul Barry, Apr 14 2005

Status

approved