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A350534
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Sum of the largest parts of the partitions of n into 3 parts whose largest part is equal to the product of the other two.
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2
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0, 0, 0, 1, 0, 2, 0, 3, 4, 4, 0, 11, 0, 6, 8, 16, 0, 18, 0, 21, 12, 10, 0, 40, 16, 12, 16, 31, 0, 52, 0, 36, 20, 16, 24, 88, 0, 18, 24, 74, 0, 76, 0, 51, 60, 22, 0, 121, 36, 60, 32, 61, 0, 100, 40, 108, 36, 28, 0, 198, 0, 30, 88, 125, 48, 124, 0, 81, 44, 140, 0, 243, 0, 36, 104
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OFFSET
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0,6
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LINKS
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FORMULA
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a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} [n-i-k = i*k] * (n-i-k), where [ ] is the Iverson bracket.
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EXAMPLE
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a(13) = 6 since we have 13 = 1+6+6, whose largest part is 6. Partitions not counted: 1+1+11, 1+2+10, 1+3+9, 1+4+8, 1+5+7, 2+2+9, 2+3+8, 2+4+7, 2+5+6, 3+3+7, 3+4+6, 3+5+5, 4+4+5.
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MATHEMATICA
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Table[Sum[Sum[(n - i - k) KroneckerDelta[(n - i - k), (i*k)], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 0, 100}]
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PROG
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(PARI) first(n) = {my(res = vector(n)); for(i = 1, n \ 2, for(j = i, n\i, c = i + j + i*j; if(c <= n, res[c] += i*j))); concat(0, res)} \\ David A. Corneth, Jan 07 2022
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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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