A308762 Sum of the third largest parts of the partitions of n into 4 squarefree parts.

0, 0, 0, 0, 1, 1, 2, 3, 6, 6, 10, 11, 16, 16, 22, 23, 35, 38, 51, 57, 75, 76, 94, 99, 125, 128, 158, 162, 208, 209, 242, 251, 311, 317, 376, 390, 467, 478, 548, 553, 672, 682, 784, 801, 957, 957, 1096, 1101, 1284, 1294, 1471, 1469, 1725, 1717, 1917, 1918

Offset

0,7

Links

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

Index entries for sequences related to partitions

Formula

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

a(n) = A308783(n) - A308768(n) - A308769(n) - A308770(n).

Mathematica

Table[Sum[Sum[Sum[j * MoebiusMu[k]^2*MoebiusMu[j]^2*MoebiusMu[i]^2* MoebiusMu[n - i - j - k]^2, {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]

Crossrefs

Cf. A008683, A308767, A308768, A308769, A308770, A308783.

Sequence in context: A185423 A144583 A328565 * A155215 A363075 A119319

Adjacent sequences: A308759 A308760 A308761 * A308763 A308764 A308765

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 23 2019

Status

approved