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A308843 Sum of the third largest parts in the partitions of n into 5 squarefree parts. 5
0, 0, 0, 0, 0, 1, 1, 2, 3, 6, 8, 12, 13, 21, 23, 32, 33, 49, 56, 77, 86, 117, 130, 162, 174, 223, 239, 295, 312, 391, 418, 497, 520, 631, 675, 801, 844, 1009, 1072, 1247, 1306, 1537, 1628, 1890, 1972, 2312, 2425, 2786, 2889, 3325, 3472, 3955, 4089, 4671, 4851, 5474 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Conjecture: a(4*k + 3) < a(4*k + 4) for 4*k + 3 >= 195. This conjecture holds for all terms in the b-file. - David A. Corneth, Sep 16 2019

LINKS

David A. Corneth, Table of n, a(n) for n = 0..1000

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-l)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k-l)^2 * j, where mu is the Möbius function (A008683).

a(n) = A308839(n) - A308841(n) - A308842(n) - A308844(n) - A308845(n).

MATHEMATICA

Table[Sum[Sum[Sum[Sum[j * MoebiusMu[l]^2*MoebiusMu[k]^2*MoebiusMu[j]^2 *MoebiusMu[i]^2*MoebiusMu[n - i - j - k - l]^2, {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {n, 0, 50}]

CROSSREFS

Cf. A008683, A308839, A308840, A308841, A308842, A308844, A308845.

Sequence in context: A280094 A025053 A140496 * A086552 A098393 A263883

Adjacent sequences:  A308840 A308841 A308842 * A308844 A308845 A308846

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jun 28 2019

EXTENSIONS

a(54)..a(55) from David A. Corneth, Sep 16 2019

STATUS

approved

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Last modified August 13 05:41 EDT 2020. Contains 336442 sequences. (Running on oeis4.)