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A000742 Number of compositions of n into 4 ordered relatively prime parts.
(Formerly M3381 N1362)
8

%I M3381 N1362

%S 1,4,10,20,34,56,80,120,154,220,266,360,420,560,614,816,884,1120,1210,

%T 1540,1572,2020,2080,2544,2638,3276,3200,4060,4040,4840,4896,5960,

%U 5710,7140,6954,8216,8136,9880,9244,11480,11010,12824,12650,15180,14024,17276

%N Number of compositions of n into 4 ordered relatively prime parts.

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

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

%H Marius A. Burtea, <a href="/A000742/b000742.txt">Table of n, a(n) for n = 4..10000</a>

%H H. W. Gould, <a href="http://www.fq.math.ca/Scanned/2-4/gould.pdf">Binomial coefficients, the bracket function and compositions with relatively prime summands</a>, Fib. Quart. 2(4) (1964), 241-260.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F Möbius transform of C(n-1,3).

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

%p with(numtheory):

%p a:= n-> add(mobius(n/d)*binomial(d-1, 3), d=divisors(n)):

%p seq(a(n), n=4..50); # _Alois P. Heinz_, Feb 05 2020

%t 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 *)

%o (MAGMA) [&+[MoebiusMu(n div d)*Binomial(d-1, 3):d in Divisors(n)]:n in[4..49]]; // _Marius A. Burtea_, Feb 08 2020

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

%K nonn

%O 4,2

%A _N. J. A. Sloane_.

%E Offset changed to 4 by _Ilya Gutkovskiy_, Feb 05 2020

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Last modified August 8 04:12 EDT 2020. Contains 336290 sequences. (Running on oeis4.)