A327628 Number of parts in all thrice partitions of n into distinct parts.

0, 1, 1, 7, 16, 35, 73, 170, 357, 799, 1583, 3159, 6395, 12669, 24663, 49001, 92907, 176482, 340322, 637803, 1189953, 2241558, 4156837, 7629834, 14120680, 25810341, 47076266, 85790799, 155030395, 279010877, 505264895, 902632836, 1611104709, 2880345715

Offset: 0

Author

Alois P. Heinz, Sep 19 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..3000
• Wikipedia, Partition (number theory)

Crossrefs

Column k=3 of A327622.

Cf. A327627.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(n=0, [1, 0],
     `if`(k=0, [1, 1], `if`(i*(i+1)/2 (f-> f +[0, f[1]*h[2]/h[1]])(h[1]*
        b(n-i, min(n-i, i-1), k)))(b(i$2, k-1)))))
    end:
a:= n-> b(n$2, 3)[2]:
seq(a(n), n=0..35);

Mathematica

b[n_, i_, k_] := b[n, i, k] = With[{}, If[n == 0, Return[{1, 0}]]; If[k == 0, Return[{1, 1}]]; If[i(i+1)/2 < n, Return[{0, 0}]]; b[n, i - 1, k] + Function[h, Function[f, f + {0, f[[1]] h[[2]]/h[[1]]}][h[[1]] b[n - i, Min[n - i, i - 1], k]]][b[i, i, k - 1]]];
a[n_] := b[n, n, 3][[2]];
a /@ Range[0, 35] (* Jean-François Alcover, Dec 09 2020, after Alois P. Heinz *)