A000742 Number of compositions of n into 4 ordered relatively prime parts. (Formerly M3381 N1362)

1, 4, 10, 20, 34, 56, 80, 120, 154, 220, 266, 360, 420, 560, 614, 816, 884, 1120, 1210, 1540, 1572, 2020, 2080, 2544, 2638, 3276, 3200, 4060, 4040, 4840, 4896, 5960, 5710, 7140, 6954, 8216, 8136, 9880, 9244, 11480, 11010, 12824, 12650, 15180, 14024, 17276

Offset

4,2

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Marius A. Burtea, Table of n, a(n) for n = 4..10000

H. W. Gould, Binomial coefficients, the bracket function and compositions with relatively prime summands, Fib. Quart. 2(4) (1964), 241-260.

N. J. A. Sloane, Transforms

Formula

Möbius transform of C(n-1,3).

G.f.: Sum_{k>=1} mu(k) * x^(4*k) / (1 - x^k)^4. - Ilya Gutkovskiy, Feb 05 2020

Maple

with(numtheory):
a:= n-> add(mobius(n/d)*binomial(d-1, 3), d=divisors(n)):
seq(a(n), n=4..50);  # Alois P. Heinz, Feb 05 2020

Mathematica

a[n_] := Sum[Boole[Divisible[n, k]] MoebiusMu[n/k] Binomial[k - 1, 3], {k, 1, n}]; Table[a[n], {n, 4, 51}] (* Jean-François Alcover, Feb 11 2016 *)

Prog

(Magma) [&+[MoebiusMu(n div d)*Binomial(d-1, 3):d in Divisors(n)]:n in[4..49]]; // Marius A. Burtea, Feb 08 2020

Crossrefs

Cf. A000741, A000743, A023031, A023032, A023033, A023034, A023035.

Sequence in context: A008013 A301154 A024991 * A362419 A301134 A132152

Adjacent sequences: A000739 A000740 A000741 * A000743 A000744 A000745

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Offset changed to 4 by Ilya Gutkovskiy, Feb 05 2020

Status

approved