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 A308902 Number of partitions of n into 6 squarefree parts. 10
 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 8, 8, 11, 13, 18, 19, 25, 27, 36, 39, 48, 52, 66, 70, 85, 91, 111, 117, 139, 148, 176, 185, 214, 227, 266, 278, 318, 336, 387, 405, 459, 482, 550, 574, 644, 676, 764, 796, 885, 929, 1038, 1082, 1194, 1247, 1385, 1440, 1580 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 LINKS Table of n, a(n) for n=0..58. 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, where mu is the Möbius function (A008683). a(n) = A308903(n)/n. MATHEMATICA Table[Sum[Sum[Sum[Sum[Sum[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, A308903, A308906, A308907, A308908, A308909, A308910, A308911. Sequence in context: A296561 A300121 A267046 * A166515 A339560 A360142 Adjacent sequences: A308899 A308900 A308901 * A308903 A308904 A308905 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Jun 29 2019 STATUS approved

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Last modified June 17 13:47 EDT 2024. Contains 373445 sequences. (Running on oeis4.)