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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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
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
Sequence in context: A338847 A032020 A261962 * A084656 A073749 A299590
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 22 2018
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)