A308907 Sum of the fifth largest parts in the partitions of n into 6 squarefree parts.

0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 6, 10, 10, 14, 18, 26, 28, 37, 41, 57, 62, 77, 87, 113, 122, 152, 170, 213, 230, 279, 307, 376, 402, 471, 516, 622, 661, 768, 830, 978, 1041, 1194, 1282, 1492, 1586, 1804, 1932, 2217, 2340, 2632, 2815, 3195, 3380, 3780, 4026

Offset

0,9

Links

Table of n, a(n) for n=0..55.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-k-j-l-m)^2 * l, where mu is the Möbius function (A008683).

a(n) = A308903(n) - A308906(n) - A308908(n) - A308909(n) - A308910(n) - A308911(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[l*MoebiusMu[i]^2*MoebiusMu[j]^2*MoebiusMu[k]^2* MoebiusMu[l]^2*MoebiusMu[m]^2*MoebiusMu[n - i - j - k - l - m]^2, {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]

Crossrefs

Cf. A008683, A308902, A308903, A308906, A308908, A308909, A308910, A308911.

Sequence in context: A071058 A076178 A347693 * A285908 A060988 A359744

Adjacent sequences: A308904 A308905 A308906 * A308908 A308909 A308910

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 29 2019

Status

approved