A023034 Number of compositions of n into 9 ordered relatively prime parts.

1, 9, 45, 165, 495, 1287, 3003, 6435, 12870, 24309, 43758, 75573, 125970, 203445, 319770, 490149, 735471, 1081080, 1562274, 2218788, 3108105, 4289133, 5852925, 7882290, 10518255, 13871286, 18156204, 23511345, 30260340, 38564262, 48902997

Offset

9,2

Links

Marius A. Burtea, Table of n, a(n) for n = 9..5000

N. J. A. Sloane, Transforms

Formula

Moebius transform of C(n-1,8).

G.f.: Sum_{k>=1} mu(k) * x^(9*k) / (1 - x^k)^9. - Ilya Gutkovskiy, Feb 05 2020

Maple

with(numtheory):
a:= n-> add(mobius(n/d)*binomial(d-1, 8), d=divisors(n)):
seq(a(n), n=9..50);  # Alois P. Heinz, Feb 05 2020

Mathematica

Table[a[n], {n, 9, 45}]a[n_]:=DivisorSum[n, Binomial[#-1, 8] MoebiusMu[n/#]&]; Array[a, 37, 9] (* or *) a[n_]:=Sum[Boole[Divisible[n, k]] MoebiusMu[n/k] Binomial[k-1, 8], {k, 1, n}]; Table[a[n], {n, 9, 45}] (* Vincenzo Librandi, Feb 08 2020 *)

Prog

(Magma) [&+[MoebiusMu(n div d)*Binomial(d-1, 8):d in Divisors(n)]:n in[9..39]]; // Marius A. Burtea, Feb 07 2020

Crossrefs

Cf. A000741, A000742, A000743, A023031, A023032, A023033, A023035.

Sequence in context: A306942 A289354 A008491 * A000581 A306939 A229889

Adjacent sequences: A023031 A023032 A023033 * A023035 A023036 A023037

Keyword

nonn

Author

David W. Wilson

Status

approved