A105597 -id:A105597 - cp's OEIS frontend

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

Paul Barry, Apr 14 2005

Central column of A105586. Partial sums are A105235.

Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for characteristic functions

Cf. A105235, A105586.

Cf. A008683, A105597.

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

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

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

A105598 Partial sums of central numbers for a Moebius-binomial triangle.

Original entry on oeis.org

1, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14, 15, 16, 17, 18, 18, 19, 20, 21, 22, 23, 24, 24, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 39, 39, 40, 41, 42, 43, 44, 45, 45, 46, 47, 48, 49, 50, 51, 52, 52, 53, 54, 54, 55, 56, 57, 58, 58, 59, 60, 61, 62

Offset: 0

Paul Barry, Apr 15 2005

Partial sums of A105597.

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Accumulate[Table[Binomial[Abs[MoebiusMu[x]],Abs[MoebiusMu[Floor[x/2]]]],{x,0,80}]] (* Harvey P. Dale, Mar 13 2014 *)

a(n)=sum{k=0..n, binomial(abs(mu(k)), abs(mu(floor(k/2))))}

cp's OEIS Frontend

A105234 Central column of a Moebius-binomial triangle.

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