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A308953 Sum of all the parts in the partitions of n into 7 squarefree parts. 8
0, 0, 0, 0, 0, 0, 0, 7, 8, 18, 20, 44, 60, 104, 126, 180, 224, 340, 396, 551, 640, 882, 1034, 1357, 1536, 2025, 2314, 2943, 3304, 4176, 4680, 5797, 6464, 7887, 8806, 10605, 11664, 14023, 15504, 18291, 20040, 23657, 25956, 30272, 32956, 38295, 41860, 48269 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..47.

Index entries for sequences related to partitions

FORMULA

a(n) = 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(o)^2 * mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k-l-m-o)^2, where mu is the Möbius function (A008683).

a(n) = n * A308952(n).

a(n) = A308954(n) + A308955(n) + A308956(n) + A308957(n) + A308958(n) + A308959(n) + A308960(n).

MATHEMATICA

Table[n*Sum[Sum[Sum[Sum[Sum[Sum[MoebiusMu[o]^2 * MoebiusMu[m]^2 * MoebiusMu[l]^2 * MoebiusMu[k]^2 * MoebiusMu[j]^2 * MoebiusMu[i]^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, A308952, A308954, A308955, A308956, A308957, A308958, A308959, A308960.

Sequence in context: A214788 A155946 A144614 * A143504 A322636 A309482

Adjacent sequences:  A308950 A308951 A308952 * A308954 A308955 A308956

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jul 03 2019

STATUS

approved

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Last modified January 19 05:41 EST 2022. Contains 350464 sequences. (Running on oeis4.)