A327627 Number of parts in all thrice partitions of n.

0, 1, 7, 25, 109, 315, 1179, 3234, 10789, 29517, 89217, 238422, 708782, 1838147, 5158957, 13489966, 36783238, 94122716, 252156677, 638254389, 1674465026, 4215683662, 10834938301, 27032106456, 68911496918, 170196098655, 427274190051, 1051046411165, 2612004809769

Offset: 0

Author

Alois P. Heinz, Sep 19 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000

Crossrefs

Column k=3 of A327618.

Cf. A327628.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(n=0, [1, 0],
     `if`(k=0, [1, 1], `if`(i<2, 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), k)))(b(i$2, k-1))))
    end:
a:= n-> b(n$2, 3)[2]:
seq(a(n), n=0..30);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n == 0, {1, 0}, If[k == 0, {1, 1}, If[i < 2, 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], k]]][b[i, i, k - 1]]]];
a[n_] := b[n, n, 3][[2]];
a /@ Range[0, 30] (* Jean-François Alcover, Dec 10 2020, after Alois P. Heinz *)