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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 (list; graph; refs; listen; history; text; internal format)
 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 * A301134 A132152 A008234 Adjacent sequences:  A000739 A000740 A000741 * A000743 A000744 A000745 KEYWORD nonn AUTHOR EXTENSIONS Offset changed to 4 by Ilya Gutkovskiy, Feb 05 2020 STATUS approved

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Last modified May 16 04:38 EDT 2022. Contains 353688 sequences. (Running on oeis4.)