A105235 Partial sums of the central column of a Moebius-binomial triangle.

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

Offset: 0

Author

Paul Barry, Apr 14 2005

Keywords

• easy
• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..10000

Crossrefs

Partial sums of A105234.

Cf. A008683.

Programs

Mathematica

a[n_]:=Binomial[Abs[MoebiusMu[2n]],Abs[MoebiusMu[n]]];Accumulate[Table[a[n],{n,0,72}]] (* James C. McMahon, Jan 22 2024 *)

PARI

seq(n) = {my(v=vector(1+n)); v[1]=1; for(k=1, n, v[1+k] = v[k] + binomial(abs(moebius(2*k)), abs(moebius(k)))); v} \\ Andrew Howroyd, Jan 22 2024

Formula

a(n) = 1 + Sum_{k=1..n} binomial(abs(mu(2*k)), abs(mu(k))).