A320374 Number of parts in all partitions of n with largest multiplicity four.

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

Offset

4,1

Links

Alois P. Heinz, Table of n, a(n) for n = 4..1000

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

Adjacent sequences: A320371 A320372 A320373 * A320375 A320376 A320377

Keyword

nonn

Author

Alois P. Heinz, Oct 11 2018

Status

approved