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A000741 Number of compositions of n into 3 ordered relatively prime parts.
(Formerly M2531 N0999)
13
0, 0, 1, 3, 6, 9, 15, 18, 27, 30, 45, 42, 66, 63, 84, 84, 120, 99, 153, 132, 174, 165, 231, 180, 270, 234, 297, 270, 378, 276, 435, 360, 450, 408, 540, 414, 630, 513, 636, 552, 780, 558, 861, 690, 828, 759, 1035, 744, 1113, 870, 1104, 972, 1326, 945, 1380, 1116, 1386, 1218 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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

Alois P. Heinz, Table of n, a(n) for n = 1..10000

H. W. Gould, Binomial coefficients, the bracket function and compositions with relatively prime summands, Fib. Quart. 2(4) (1964), 241-260.

C. Kimberling, Matrix Transformations of Integer Sequences, J. Integer Seqs., Vol. 6, 2003.

N. J. A. Sloane, Transforms

FORMULA

Moebius transform of A000217(n-2).

G.f.: 1 + Sum_{n>=1} a(n)*x^n/(1 - x^n) = (1 - 3*x + 3*x^2)/(1 - x)^3. - Ilya Gutkovskiy, Apr 26 2017

MAPLE

with (numtheory):

mobtr:= proc(p)

          proc(n) option remember;

            add (mobius(n/d)*p(d), d=divisors(n))

          end

        end:

A000217:= n-> n*(n+1)/2:

a:= mobtr (n-> A000217(n-2)):

seq (a(n), n=1..58);  # Alois P. Heinz, Feb 08 2011

MATHEMATICA

mobtr[p_] := Module[{f}, f[n_] := f[n] = Sum[MoebiusMu[n/d]*p[d], {d, Divisors[n]}]; f]; A000217[n_] := n*(n+1)/2; a = mobtr[A000217[#-2]&]; Table[a[n], {n, 1, 58}] (* Jean-Fran├žois Alcover, Mar 12 2014, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A133331 A276381 A259728 * A133205 A049991 A143981

Adjacent sequences:  A000738 A000739 A000740 * A000742 A000743 A000744

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Edited by Alois P. Heinz, Feb 08 2011

STATUS

approved

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Last modified July 13 07:30 EDT 2020. Contains 335676 sequences. (Running on oeis4.)