A308908 Sum of the fourth largest parts in the partitions of n into 6 squarefree parts.

0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 5, 7, 11, 12, 18, 22, 32, 34, 47, 52, 71, 78, 102, 116, 154, 170, 217, 243, 305, 329, 406, 445, 546, 587, 702, 768, 921, 982, 1147, 1240, 1459, 1562, 1811, 1948, 2260, 2401, 2748, 2943, 3387, 3596, 4087, 4381, 4987, 5288, 5959

Offset

0,9

Links

Table of n, a(n) for n=0..54.

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

a(n) = A308903(n) - A308906(n) - A308907(n) - A308909(n) - A308910(n) - A308911(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[k*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, A308909, A308910, A308911.

Sequence in context: A278388 A239737 A262883 * A259446 A265769 A308957

Adjacent sequences: A308905 A308906 A308907 * A308909 A308910 A308911

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 29 2019

Status

approved