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

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..3000

Wikipedia, Partition (number theory)

Maple

b:= proc(n, i, k) option remember; `if`(n=0, [1, 0],
     `if`(k=0, [1, 1], `if`(i*(i+1)/2<n, 0, b(n, i-1, k)+
         (h-> (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 *)

Crossrefs

Column k=3 of A327622.

Cf. A327627.

Sequence in context: A301721 A176449 A278945 * A169877 A286710 A036834

Adjacent sequences: A327625 A327626 A327627 * A327629 A327630 A327631

Keyword

nonn

Author

Alois P. Heinz, Sep 19 2019

Status

approved