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A308910 revision #6

A308910

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

0, 0, 0, 0, 0, 0, 1, 1, 3, 4, 8, 10, 18, 20, 32, 38, 60, 70, 100, 112, 157, 181, 231, 259, 341, 382, 479, 531, 672, 743, 917, 1013, 1253, 1378, 1658, 1819, 2205, 2392, 2832, 3065, 3638, 3909, 4572, 4890, 5726, 6104, 7027, 7495, 8656, 9187, 10455, 11130

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OFFSET

0,9

LINKS

Table of n, a(n) for n=0..51.

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 * i, where mu is the Möbius function (A008683).

a(n) = A308903(n) - A308906(n) - A308907(n) - A308908(n) - A308909(n) - A308911(n).

MATHEMATICA

Table[Sum[Sum[Sum[Sum[Sum[i*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, A308907, A308908, A308909, A308911.

Sequence in context: A355193 A238546 A147617 * A308959 A326451 A263982

Adjacent sequences: A308907 A308908 A308909 * A308911 A308912 A308913

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jun 29 2019

STATUS

proposed