A280198 Expansion of 1/(1 - Sum_{k>=1} mu(2*k-1)^2*x^(2*k-1)), where mu() is the Moebius function (A008683).

1, 1, 1, 2, 3, 5, 8, 13, 21, 33, 53, 86, 138, 222, 357, 574, 923, 1484, 2387, 3839, 6173, 9927, 15964, 25672, 41284, 66389, 106762, 171686, 276091, 443989, 713988, 1148179, 1846411, 2969252, 4774918, 7678647, 12348195, 19857396, 31933099, 51352294, 82580715, 132799801, 213558181, 343427445, 552272966, 888121883, 1428207656

Offset

0,4

Comments

Number of compositions (ordered partitions) into odd squarefree parts (A056911).

Links

Table of n, a(n) for n=0..46.

Eric Weisstein's World of Mathematics, Squarefree

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{k>=1} mu(2*k-1)^2*x^(2*k-1)).

Example

a(4) = 3 because we have [3, 1], [1, 3] and [1, 1, 1, 1].

Mathematica

nmax = 46; CoefficientList[Series[1/(1 - Sum[MoebiusMu[2 k - 1]^2 x^(2 k - 1), {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A005117, A008683, A056911, A134345, A280194.

Sequence in context: A181600 A111917 A309676 * A175712 A013986 A121343

Adjacent sequences: A280195 A280196 A280197 * A280199 A280200 A280201

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 28 2016

Status

approved