A341069 Number of ways to write n as an ordered sum of 9 squarefree numbers.

1, 9, 45, 156, 423, 963, 1959, 3708, 6669, 11410, 18594, 29052, 44046, 65196, 94284, 133104, 184248, 251406, 338995, 450936, 591885, 768657, 990567, 1265832, 1602273, 2010294, 2506572, 3107136, 3825675, 4676643, 5686347, 6882912, 8290431, 9928305, 11834289, 14052816, 16624846

Offset

9,2

Links

Table of n, a(n) for n=9..45.

Formula

G.f.: (Sum_{k>=1} mu(k)^2 * x^k)^9.

Maple

b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add(
      `if`(numtheory[issqrfree](j), b(n-j, t-1), 0), j=1..n)))
    end:
a:= n-> b(n, 9):
seq(a(n), n=9..45);  # Alois P. Heinz, Feb 04 2021

Mathematica

nmax = 45; CoefficientList[Series[Sum[MoebiusMu[k]^2 x^k, {k, 1, nmax}]^9, {x, 0, nmax}], x] // Drop[#, 9] &

Crossrefs

Cf. A005117, A008683, A008966, A098235, A280210, A326522, A341064, A341065, A341066, A341067, A341068, A341070.

Sequence in context: A095166 A357717 A341988 * A126899 A162602 A247609

Adjacent sequences: A341066 A341067 A341068 * A341070 A341071 A341072

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 04 2021

Status

approved