A308909 Sum of the third largest parts in the partitions of n into 6 squarefree parts.

0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 6, 8, 14, 15, 23, 28, 39, 43, 62, 70, 98, 115, 152, 175, 227, 253, 319, 356, 441, 485, 599, 656, 793, 864, 1026, 1121, 1344, 1453, 1709, 1865, 2184, 2357, 2747, 2964, 3449, 3719, 4289, 4618, 5330, 5693, 6494, 6956, 7922, 8430

Offset

0,9

Links

Table of n, a(n) for n=0..53.

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

a(n) = A308903(n) - A308906(n) - A308907(n) - A308908(n) - A308910(n) - A308911(n).

Mathematica

Table[Total[Select[IntegerPartitions[n, {6}], AllTrue[#, SquareFreeQ]&][[All, 3]]], {n, 0, 60}] (* Harvey P. Dale, Jan 31 2022 *)

Crossrefs

Cf. A008683, A308902, A308903, A308906, A308907, A308908, A308910, A308911.

Sequence in context: A004101 A003405 A153918 * A369356 A308958 A326450

Adjacent sequences: A308906 A308907 A308908 * A308910 A308911 A308912

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 29 2019

Status

approved