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

0,3

Links

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

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 *)

Crossrefs

Column k=3 of A327618.

Cf. A327628.

Sequence in context: A155271 A200152 A255280 * A110240 A266810 A199893

Adjacent sequences: A327624 A327625 A327626 * A327628 A327629 A327630

Keyword

nonn

Author

Alois P. Heinz, Sep 19 2019

Status

approved