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A280210
Expansion of (Sum_{k>=1} mu(k)^2*x^k)^3, where mu(k) is the Moebius function (A008683).
10
0, 0, 0, 1, 3, 6, 7, 9, 12, 19, 21, 21, 21, 30, 36, 37, 36, 48, 58, 63, 57, 70, 78, 87, 78, 96, 105, 114, 105, 123, 133, 138, 126, 148, 162, 174, 156, 195, 207, 220, 192, 234, 250, 261, 237, 280, 312, 318, 282, 330, 363, 370, 315, 375, 405, 432, 366, 421, 453, 483, 417, 468, 507, 532, 474, 537, 568, 591, 519, 601, 630, 666, 570
OFFSET
0,5
COMMENTS
Number of ordered ways of writing n as sum of three squarefree numbers (A005117).
LINKS
Eric Weisstein's World of Mathematics, Squarefree
FORMULA
G.f.: (Sum_{k>=1} mu(k)^2*x^k)^3.
EXAMPLE
a(4) = 3 because we have [2, 1, 1], [1, 2, 1] and [1, 1, 2].
MATHEMATICA
nmax = 72; CoefficientList[Series[(Sum[MoebiusMu[k]^2 x^k, {k, 1, nmax}])^3, {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 29 2016
STATUS
approved