A301500 Number of compositions (ordered partitions) of n into squarefree parts (A005117) such that no two adjacent parts are equal (Carlitz compositions).

1, 1, 1, 3, 3, 5, 11, 15, 25, 45, 69, 115, 193, 309, 513, 849, 1387, 2291, 3771, 6189, 10195, 16773, 27579, 45391, 74675, 122837, 202111, 332507, 547011, 899949, 1480583, 2435803, 4007361, 6592863, 10846405, 17844319, 29357197, 48297813, 79458705, 130724101, 215064673

Offset

0,4

Links

Table of n, a(n) for n=0..40.

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{k>=1} mu(k)^2*x^k/(1 + x^k)), where mu() is the Moebius function (A008683).

Example

a(5) = 5 because we have [5], [3, 2], [2, 3], [2, 1, 2] and [1, 3, 1].

Mathematica

nmax = 40; CoefficientList[Series[1/(1 - Sum[MoebiusMu[k]^2 x^k/(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A003242, A005117, A008683, A280194, A301428, A301501.

Sequence in context: A338847 A032020 A261962 * A084656 A073749 A299590

Adjacent sequences: A301497 A301498 A301499 * A301501 A301502 A301503

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 22 2018

Status

approved