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A308767 Number of partitions of n into 4 squarefree parts. 5
0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 6, 6, 8, 8, 11, 11, 15, 15, 19, 20, 25, 24, 30, 30, 37, 36, 44, 43, 53, 52, 60, 60, 71, 69, 80, 80, 93, 92, 106, 104, 122, 119, 135, 134, 155, 152, 172, 172, 194, 192, 213, 212, 239, 234, 257, 256, 290, 281, 308, 305, 343, 336 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..61.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k)^2, where mu is the Möbius function (A008683).

a(n) = A308783(n)/n.

MATHEMATICA

Table[Sum[Sum[Sum[MoebiusMu[k]^2*MoebiusMu[j]^2*MoebiusMu[i]^2*MoebiusMu[n - i - j - k]^2, {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]

CROSSREFS

Cf. A008683, A308783.

Sequence in context: A131055 A052928 A137501 * A285999 A005186 A259881

Adjacent sequences:  A308764 A308765 A308766 * A308768 A308769 A308770

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jun 23 2019

STATUS

approved

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Last modified November 17 08:39 EST 2019. Contains 329217 sequences. (Running on oeis4.)