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