cp's OEIS Frontend

A179817 Maximally refined partitions into distinct parts (of any natural number) with n parts.

%I A179817 #10 Apr 14 2021 18:15:03
%S A179817 1,2,4,8,14,27,48,86,151,269,460,808,1386,2372,4048,6890,11661,19719,
%T A179817 33167,55705,93288,155954,260040,432895,719252,1192989,1975724,
%U A179817 3267513,5396171,8900534,14663096
%N A179817 Maximally refined partitions into distinct parts (of any natural number) with n parts.
%C A179817 For the definition, see sequence A179009. This sequence counts the same objects using a different statistic, the number of parts rather than their sum.
%e A179817 For n=2, the partitions being counted are:
%e A179817   2+1, 3+1, 4+1, 3+2.
%e A179817 For n=3, the partitions are:
%e A179817   3+2+1, 4+2+1, 5+2+1, 6+2+1,
%e A179817   4+3+1, 5+3+1, 6+4+1, 4+3+2.
%o A179817 (PARI)
%o A179817 ok(k,b)={for(i=1, (k-1)\2, if(bittest(b,i) && bittest(b,k-i), return(0))); 1}
%o A179817 a(n)={((k,w,b)->if(w==n, 1, if(k<=2*w+1, self()(k+1, w, bitor(b,1<<k))) + if(ok(k,b), self()(k+1, w+1, b))))(1,0,0)} \\ _Andrew Howroyd_, Apr 14 2021
%Y A179817 Cf. A179009, A179822.
%K A179817 nonn,more
%O A179817 0,2
%A A179817 _Moshe Shmuel Newman_, Jan 10 2011
%E A179817 a(0)=1 prepended and a(19)-a(30) from _Andrew Howroyd_, Apr 14 2021