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A320374 Number of parts in all partitions of n with largest multiplicity four. 2
4, 0, 5, 5, 15, 16, 30, 36, 60, 75, 116, 149, 217, 273, 386, 491, 664, 839, 1116, 1399, 1829, 2292, 2937, 3656, 4638, 5729, 7187, 8840, 10984, 13430, 16558, 20138, 24657, 29846, 36288, 43736, 52880, 63430, 76289, 91159, 109106, 129841, 154724, 183452, 217727 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,1
LINKS
FORMULA
a(n) ~ 3^(1/4) * log(5) * exp(2*Pi*sqrt(2*n/15)) / (2^(5/4) * 5^(1/4) * Pi * n^(1/4)). - Vaclav Kotesovec, Oct 25 2018
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
add((l->l+[0, l[1]*j])(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])(4):
seq(a(n), n=4..50);
MATHEMATICA
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 = 4}, (b[n, n, k] - b[n, n, k - 1])[[2]]];
a /@ Range[4, 60] (* Jean-François Alcover, Dec 13 2020, after Alois P. Heinz *)
CROSSREFS
Column k=4 of A213177.
Sequence in context: A268631 A335775 A308108 * A264757 A195773 A153018
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 11 2018
STATUS
approved

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Last modified April 18 09:20 EDT 2024. Contains 371769 sequences. (Running on oeis4.)