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A320612
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Number of parts in all partitions of n in which no part occurs more than nine times.
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3
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1, 3, 6, 12, 20, 35, 54, 86, 128, 182, 264, 376, 520, 718, 978, 1318, 1761, 2338, 3070, 4008, 5206, 6707, 8604, 10982, 13933, 17604, 22155, 27745, 34627, 43061, 53338, 65859, 81074, 99458, 121687, 148469, 180633, 219202, 265386, 320473, 386147, 464245, 556925
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) ~ log(10) * exp(Pi*sqrt(3*n/5)) / (2 * Pi * 15^(1/4) * n^(1/4)). - Vaclav Kotesovec, Oct 18 2018
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(9*i*(i+1)/2<n, 0, add(
(l-> [0, l[1]*j]+l)(b(n-i*j, min(n-i*j, i-1))), j=0..min(n/i, 9))))
end:
a:= n-> b(n$2)[2]:
seq(a(n), n=1..50);
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MATHEMATICA
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Table[Length[ Flatten[Select[IntegerPartitions[n], Max[Tally[#][[All, 2]]] <= 9 &]]], {n, 43}] (* Robert Price, Jul 31 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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