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A320608
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Number of parts in all partitions of n in which no part occurs more than five times.
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3
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1, 3, 6, 12, 20, 29, 47, 71, 104, 150, 213, 292, 405, 547, 736, 977, 1292, 1688, 2198, 2834, 3638, 4636, 5890, 7431, 9347, 11684, 14564, 18067, 22348, 27531, 33813, 41378, 50504, 61438, 74561, 90208, 108896, 131096, 157485, 188717, 225682, 269285, 320691
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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(6) * exp(Pi*sqrt(5*n)/3) / (2 * Pi * 5^(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`(5*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, 5))))
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]]] <= 5 &]]], {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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