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A320373
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Number of parts in all partitions of n with largest multiplicity three.
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2
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3, 0, 4, 7, 13, 14, 27, 33, 55, 72, 107, 137, 196, 250, 344, 442, 588, 750, 982, 1234, 1591, 1992, 2523, 3135, 3944, 4857, 6035, 7408, 9121, 11109, 13599, 16465, 20004, 24122, 29112, 34927, 41952, 50078, 59836, 71169, 84625, 100219, 118716, 140061, 165225
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OFFSET
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3,1
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LINKS
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FORMULA
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a(n) ~ log(2) * exp(Pi*sqrt(n/2)) / (Pi * 2^(1/4) * n^(1/4)). - Vaclav Kotesovec, Oct 25 2018
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MAPLE
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b:= proc(n, i, k) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
add((l-> [0, l[1]*j]+l)(b(n-i*j, i-1, k)), j=0..min(n/i, k))))
end:
a:= n-> (k-> (b(n$2, k)-b(n$2, k-1))[2])(3):
seq(a(n), n=3..60);
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MATHEMATICA
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b[n_, i_, k_] := b[n, i, k] = If[n == 0, {1, 0}, If[i < 1, {0, 0}, Sum[Function[l, {0, l[[1]] j} + l][b[n - i j, i - 1, k]], {j, 0, Min[n/i, k]}]]];
a[n_] := With[{k = 3}, (b[n, n, k] - b[n, n, k - 1])[[2]]];
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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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