|
%I #9 Dec 09 2020 11:05:40
%S 0,1,1,7,16,35,73,170,357,799,1583,3159,6395,12669,24663,49001,92907,
%T 176482,340322,637803,1189953,2241558,4156837,7629834,14120680,
%U 25810341,47076266,85790799,155030395,279010877,505264895,902632836,1611104709,2880345715
%N Number of parts in all thrice partitions of n into distinct parts.
%H Alois P. Heinz, <a href="/A327628/b327628.txt">Table of n, a(n) for n = 0..3000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_(number_theory)">Partition (number theory)</a>
%p b:= proc(n, i, k) option remember; `if`(n=0, [1, 0],
%p `if`(k=0, [1, 1], `if`(i*(i+1)/2<n, 0, b(n, i-1, k)+
%p (h-> (f-> f +[0, f[1]*h[2]/h[1]])(h[1]*
%p b(n-i, min(n-i, i-1), k)))(b(i$2, k-1)))))
%p end:
%p a:= n-> b(n$2, 3)[2]:
%p seq(a(n), n=0..35);
%t 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]]];
%t a[n_] := b[n, n, 3][[2]];
%t a /@ Range[0, 35] (* _Jean-François Alcover_, Dec 09 2020, after _Alois P. Heinz_ *)
%Y Column k=3 of A327622.
%Y Cf. A327627.
%K nonn
%O 0,4
%A _Alois P. Heinz_, Sep 19 2019
|
