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A327628 Number of parts in all thrice partitions of n into distinct parts. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 19 2019
STATUS
approved

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Last modified July 23 04:43 EDT 2024. Contains 374544 sequences. (Running on oeis4.)