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A326593
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Sum of the sixth largest parts of the partitions of n into 10 parts.
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10
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 12, 17, 26, 37, 54, 73, 104, 139, 191, 253, 340, 442, 584, 749, 970, 1232, 1571, 1971, 2486, 3087, 3844, 4734, 5835, 7119, 8699, 10530, 12753, 15332, 18426, 21998, 26259, 31153, 36938, 43575, 51360, 60250
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OFFSET
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0,13
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LINKS
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Table of n, a(n) for n=0..51.
Index entries for sequences related to partitions
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FORMULA
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a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} m.
a(n) = A326588(n) - A326589(n) - A326590(n) - A326591(n) - A326592(n) - A326594(n) - A326595(n) - A326596(n) - A326597(n) - A326598(n).
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MATHEMATICA
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Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[m, {i, j, Floor[(n - j - k - l - m - o - p - q - r)/2]}], {j, k, Floor[(n - k - l - m - o - p - q - r)/3]}], {k, l, Floor[(n - l - m - o - p - q - r)/4]}], {l, m, Floor[(n - m - o - p - q - r)/5]}], {m, o, Floor[(n - o - p - q - r)/6]}], {o, p, Floor[(n - p - q - r)/7]}], {p, q, Floor[(n - q - r)/8]}], {q, r, Floor[(n - r)/9]}], {r, Floor[n/10]}], {n, 0, 50}]
Table[Total[IntegerPartitions[n, {10}][[All, 6]]], {n, 0, 60}] (* Harvey P. Dale, Dec 20 2020 *)
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CROSSREFS
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Cf. A026816, A326588, A326589, A326590, A326591, A326592, A326594, A326595, A326596, A326597, A326598.
Sequence in context: A308928 A308992 A326468 * A123569 A305651 A318185
Adjacent sequences: A326590 A326591 A326592 * A326594 A326595 A326596
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KEYWORD
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nonn
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AUTHOR
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Wesley Ivan Hurt, Jul 13 2019
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STATUS
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approved
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