cp's OEIS Frontend

A000742 Number of compositions of n into 4 ordered relatively prime parts.

%I A000742 M3381 N1362 #34 Jan 05 2025 19:51:31
%S A000742 1,4,10,20,34,56,80,120,154,220,266,360,420,560,614,816,884,1120,1210,
%T A000742 1540,1572,2020,2080,2544,2638,3276,3200,4060,4040,4840,4896,5960,
%U A000742 5710,7140,6954,8216,8136,9880,9244,11480,11010,12824,12650,15180,14024,17276
%N A000742 Number of compositions of n into 4 ordered relatively prime parts.
%D A000742 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000742 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000742 Marius A. Burtea, <a href="/A000742/b000742.txt">Table of n, a(n) for n = 4..10000</a>
%H A000742 H. W. Gould, <a href="https://web.archive.org/web/2024*/https://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 A000742 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A000742 Möbius transform of C(n-1,3).
%F A000742 G.f.: Sum_{k>=1} mu(k) * x^(4*k) / (1 - x^k)^4. - _Ilya Gutkovskiy_, Feb 05 2020
%p A000742 with(numtheory):
%p A000742 a:= n-> add(mobius(n/d)*binomial(d-1, 3), d=divisors(n)):
%p A000742 seq(a(n), n=4..50);  # _Alois P. Heinz_, Feb 05 2020
%t A000742 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 A000742 (Magma) [&+[MoebiusMu(n div d)*Binomial(d-1, 3):d in Divisors(n)]:n in[4..49]]; // _Marius A. Burtea_, Feb 08 2020
%Y A000742 Cf. A000741, A000743, A023031, A023032, A023033, A023034, A023035.
%K A000742 nonn
%O A000742 4,2
%A A000742 _N. J. A. Sloane_
%E A000742 Offset changed to 4 by _Ilya Gutkovskiy_, Feb 05 2020