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A307815 Number of partitions of n into 3 squarefree parts. 2
0, 0, 0, 1, 1, 2, 2, 3, 3, 5, 4, 5, 5, 7, 7, 9, 8, 11, 11, 13, 11, 15, 14, 18, 15, 20, 19, 23, 20, 24, 24, 27, 24, 30, 29, 34, 30, 37, 36, 42, 36, 45, 44, 50, 44, 54, 54, 59, 52, 62, 63, 68, 57, 69, 70, 78, 65, 78, 78, 88, 74, 86, 87, 98, 84, 98, 98, 107, 93, 109, 108, 120, 102, 124, 123 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from Rémy Sigrist)

Index entries for sequences related to partitions

FORMULA

a(n) = [x^n y^3] Product_{k>=1} 1/(1 - mu(k)^2*y*x^k).

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} mu(i)^2 * mu(k)^2 * mu(n-i-k)^2, where mu is the Mobius function. - Wesley Ivan Hurt, May 09 2019

EXAMPLE

a(10) = 4 because we have [7, 2, 1], [6, 3, 1], [6, 2, 2] and [5, 3, 2].

MAPLE

b:= proc(n, i) option remember; `if`(n=0, [1, 0$3], `if`(i<1, 0, b(n, i-1)+

      `if`(numtheory[issqrfree](i), [0, b(n-i, min(i, n-i))[1..3][]], 0)))

    end:

a:= n-> b(n$2)[4]:

seq(a(n), n=0..80);  # Alois P. Heinz, Apr 30 2019

MATHEMATICA

Array[Count[IntegerPartitions[#, {3}], _?(AllTrue[#, SquareFreeQ] &)] &, 75, 0]

CROSSREFS

Cf. A005117, A008683, A068307, A071068, A073576, A098235, A280210, A307727.

Sequence in context: A253554 A252463 A113605 * A070230 A007150 A213634

Adjacent sequences:  A307812 A307813 A307814 * A307816 A307817 A307818

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 30 2019

STATUS

approved

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Last modified November 22 16:31 EST 2019. Contains 329396 sequences. (Running on oeis4.)