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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 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 (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

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