

A308762


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


4



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,7


LINKS



FORMULA

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


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



KEYWORD

nonn


AUTHOR



STATUS

approved



