A320373 Number of parts in all partitions of n with largest multiplicity three.

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

Offset

3,1

Links

Alois P. Heinz, Table of n, a(n) for n = 3..5000

Formula

a(n) ~ log(2) * exp(Pi*sqrt(n/2)) / (Pi * 2^(1/4) * 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-> [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);

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 = 3}, (b[n, n, k] - b[n, n, k - 1])[[2]]];
a /@ Range[3, 60] (* Jean-François Alcover, Dec 13 2020, after Alois P. Heinz *)

Crossrefs

Column k=3 of A213177.

Sequence in context: A355977 A356581 A367480 * A303274 A199608 A128178

Adjacent sequences: A320370 A320371 A320372 * A320374 A320375 A320376

Keyword

nonn

Author

Alois P. Heinz, Oct 11 2018

Status

approved