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A308911 revision #7

A308911

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

0, 0, 0, 0, 0, 0, 1, 2, 5, 5, 13, 19, 34, 38, 55, 74, 110, 125, 173, 206, 292, 333, 433, 493, 662, 729, 929, 1034, 1323, 1441, 1770, 1955, 2403, 2598, 3096, 3376, 4066, 4360, 5121, 5566, 6584, 7064, 8183, 8832, 10326, 11021, 12626, 13592, 15701, 16743, 18957

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OFFSET

0,8

LINKS

Table of n, a(n) for n=0..50.

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 * (n-i-j-k-l-m), where mu is the Möbius function (A008683).

a(n) = A308903(n) - A308906(n) - A308907(n) - A308908(n) - A308909(n) - A308910(n).

MATHEMATICA

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

CROSSREFS

Cf. A008683, A308902, A308903, A308906, A308907, A308908, A308909, A308910.

Sequence in context: A308770 A222114 A308845 * A308960 A326452 A326532

Adjacent sequences: A308908 A308909 A308910 * A308912 A308913 A308914

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jun 29 2019

STATUS

approved