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

0,2

Links

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Partial sums of A105234.

Cf. A008683.

Sequence in context: A066530 A074183 A039960 * A073719 A105566 A064317

Adjacent sequences: A105232 A105233 A105234 * A105236 A105237 A105238

Keyword

easy,nonn

Author

Paul Barry, Apr 14 2005

Status

approved