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A000742
Number of compositions of n into 4 ordered relatively prime parts.
(Formerly M3381 N1362)
12
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
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
KEYWORD
nonn
EXTENSIONS
Offset changed to 4 by Ilya Gutkovskiy, Feb 05 2020
STATUS
approved