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A320609
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Number of parts in all partitions of n in which no part occurs more than six times.
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3
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1, 3, 6, 12, 20, 35, 47, 78, 111, 165, 228, 330, 444, 614, 820, 1108, 1452, 1930, 2491, 3255, 4175, 5366, 6802, 8665, 10880, 13705, 17089, 21336, 26401, 32716, 40207, 49458, 60452, 73863, 89780, 109101, 131902, 159415, 191864, 230741, 276470, 331021, 394970
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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(7) * exp(2*Pi*sqrt(n/7)) / (2 * Pi * 7^(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`(3*i*(i+1)<n, 0, add(
(l-> [0, l[1]*j]+l)(b(n-i*j, min(n-i*j, i-1))), j=0..min(n/i, 6))))
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]]] <= 6 &]]], {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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