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A308996
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Sum of the third largest parts in the partitions of n into 8 parts.
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8
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0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 7, 11, 19, 28, 44, 63, 92, 128, 183, 246, 337, 448, 597, 774, 1012, 1291, 1656, 2085, 2627, 3264, 4064, 4987, 6127, 7450, 9055, 10901, 13126, 15669, 18701, 22157, 26228, 30858, 36279, 42397, 49509, 57527, 66773, 77148
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OFFSET
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0,11
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LINKS
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FORMULA
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a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} j.
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MATHEMATICA
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Table[Total[IntegerPartitions[n, {8}][[All, 3]]], {n, 0, 50}] (* Harvey P. Dale, Jul 19 2020 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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