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A346760
a(n) = Sum_{d|n} mu(n/d) * binomial(d,3).
1
0, 0, 1, 4, 10, 19, 35, 52, 83, 110, 165, 196, 286, 329, 444, 504, 680, 713, 969, 1016, 1294, 1375, 1771, 1752, 2290, 2314, 2841, 2908, 3654, 3476, 4495, 4400, 5290, 5304, 6500, 6124, 7770, 7467, 8852, 8688, 10660, 9802, 12341, 11700, 13652, 13409, 16215, 14768, 18389, 17190
OFFSET
1,4
FORMULA
G.f.: Sum_{k>=1} mu(k) * x^(3*k) / (1 - x^k)^4.
a(n) = (A059376(n) - 3 * A007434(n) + 2 * A000010(n)) / 6.
MATHEMATICA
Table[Sum[MoebiusMu[n/d] Binomial[d, 3], {d, Divisors[n]}], {n, 1, 50}]
nmax = 50; CoefficientList[Series[Sum[MoebiusMu[k] x^(3 k)/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
PROG
(PARI) a(n) = sumdiv(n, d, moebius(n/d)*binomial(d, 3)); \\ Michel Marcus, Aug 03 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 02 2021
STATUS
approved