OFFSET
1,2
COMMENTS
Total number of squarefree parts in all compositions (ordered partitions) of n.
LINKS
FORMULA
G.f.: Sum_{k>=1} mu(k)^2*x^k*(1 - x)^2/(1 - 2*x)^2.
EXAMPLE
a(4) = 19 because we have [4], [3, 1], [2, 2], [2, 1, 1], [1, 3], [1, 2, 1], [1, 1, 2], [1, 1, 1, 1] and 0 + 2 + 2 + 3 + 2 + 3 + 3 + 4 = 19.
MAPLE
a:= proc(n) option remember; add(`if`(numtheory[
issqrfree](j), ceil(2^(n-j-1)), 0)+a(n-j), j=1..n)
end:
seq(a(n), n=1..33); # Alois P. Heinz, Aug 07 2019
MATHEMATICA
nmax = 33; Rest[CoefficientList[Series[Sum[MoebiusMu[k]^2 x^k (1 - x)^2/(1 - 2 x)^2, {k, 1, nmax}], {x, 0, nmax}], x]]
PROG
(PARI) x='x+O('x^34); Vec(sum(k=1, 34, moebius(k) ^2*x^k*(1 - x)^2/(1 - 2*x)^2)) \\ Indranil Ghosh, Apr 06 2017
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 06 2017
STATUS
approved