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A000742
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Number of compositions of n into 4 ordered relatively prime parts.
(Formerly M3381 N1362)
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8
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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
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OFFSET
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4,2
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REFERENCES
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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).
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LINKS
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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
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(MAGMA) [&+[MoebiusMu(n div d)*Binomial(d-1, 3):d in Divisors(n)]:n in[4..49]]; // Marius A. Burtea, Feb 08 2020
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CROSSREFS
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Cf. A000741, A000743, A023031, A023032, A023033, A023034, A023035.
Sequence in context: A008013 A301154 A024991 * A301134 A132152 A008234
Adjacent sequences: A000739 A000740 A000741 * A000743 A000744 A000745
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Offset changed to 4 by Ilya Gutkovskiy, Feb 05 2020
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STATUS
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approved
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