A308954 - OEIS

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A308954

Sum of the smallest parts in the partitions of n into 7 squarefree parts.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 8, 10, 13, 15, 22, 25, 33, 37, 49, 55, 71, 77, 98, 109, 136, 148, 182, 199, 243, 264, 314, 344, 413, 441, 522, 567, 663, 711, 829, 896, 1036, 1106, 1269, 1370, 1572, 1666, 1903, 2041, 2316, 2460, 2780, 2971, 3350, 3546

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

OFFSET

0,10

LINKS

Table of n, a(n) for n=0..56.

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(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 * o, where mu is the Möbius function (A008683).

a(n) = A308953(n) - A308955(n) - A308956(n) - A308957(n) - A308958(n) - A308959(n) - A308960(n).

MATHEMATICA

Table[Sum[Sum[Sum[Sum[Sum[Sum[o * 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, A308953, A308955, A308956, A308957, A308958, A308959, A308960.

Sequence in context: A326525 A326630 A317810 * A053097 A331443 A367411

Adjacent sequences: A308951 A308952 A308953 * A308955 A308956 A308957

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jul 03 2019

STATUS

approved