A309459 - OEIS

A309459

Number of squarefree parts in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 7, 7, 14, 20, 34, 47, 73, 98, 136, 178, 241, 305, 402, 500, 636, 782, 974, 1179, 1447, 1732, 2093, 2482, 2962, 3476, 4107, 4783, 5590, 6464, 7494, 8600, 9901, 11294, 12907, 14645, 16636, 18773, 21214, 23826, 26781, 29952, 33517, 37326

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

OFFSET

0,8

LINKS

Table of n, a(n) for n=0..48.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} (mu(i)^2 + mu(j)^2 + mu(k)^2 + mu(l)^2 + mu(m)^2 + mu(o)^2 + mu(n-i-j-k-l-m-o)^2), where mu is the Möbius function (A008683).

MATHEMATICA

Table[Sum[Sum[Sum[Sum[Sum[Sum[(MoebiusMu[i]^2 + MoebiusMu[j]^2 + MoebiusMu[k]^2 + MoebiusMu[l]^2 + MoebiusMu[m]^2 + MoebiusMu[o]^2 + MoebiusMu[n - i - j - k - l - m - o]^2), {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]

CROSSREFS

Cf. A008683.

Sequence in context: A003872 A168374 A112438 * A022090 A245426 A168379

Adjacent sequences: A309456 A309457 A309458 * A309460 A309461 A309462

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Aug 03 2019

STATUS

approved