cp's OEIS Frontend

A340651 Number of non-isomorphic cross-balanced multiset partitions of weight n.

%I A340651 #13 Jan 15 2024 20:29:17
%S A340651 1,1,2,4,11,26,77,220,677,2098,6756,22101,74264,253684,883795,3130432,
%T A340651 11275246,41240180,153117873,576634463,2201600769,8517634249,
%U A340651 33378499157,132438117118,531873247805,2161293783123,8883906870289,36928576428885,155196725172548,659272353608609,2830200765183775
%N A340651 Number of non-isomorphic cross-balanced multiset partitions of weight n.
%C A340651 We define a multiset partition to be cross-balanced if it uses exactly as many distinct vertices as the greatest size of a part.
%H A340651 Andrew Howroyd, <a href="/A340651/b340651.txt">Table of n, a(n) for n = 0..50</a>
%e A340651 Non-isomorphic representatives of the a(1) = 1 through a(5) = 16 multiset partitions:
%e A340651   {{1}}  {{1,2}}    {{1,2,3}}      {{1,2,3,4}}
%e A340651          {{1},{1}}  {{1},{2,2}}    {{1,1},{2,2}}
%e A340651                     {{2},{1,2}}    {{1,2},{1,2}}
%e A340651                     {{1},{1},{1}}  {{1,2},{2,2}}
%e A340651                                    {{1},{2,3,3}}
%e A340651                                    {{3},{1,2,3}}
%e A340651                                    {{1},{1},{2,2}}
%e A340651                                    {{1},{2},{1,2}}
%e A340651                                    {{1},{2},{2,2}}
%e A340651                                    {{2},{2},{1,2}}
%e A340651                                    {{1},{1},{1},{1}}
%o A340651 (PARI) \\ See A340652 for G.
%o A340651 seq(n)={Vec(1 + sum(k=1,n, G(k,n,k) - G(k-1,n,k) - G(k,n,k-1) + G(k-1,n,k-1)))} \\ _Andrew Howroyd_, Jan 15 2024
%Y A340651 The co-balanced version is A319616.
%Y A340651 The balanced version is A340600.
%Y A340651 The twice-balanced version is A340652.
%Y A340651 The version for factorizations is A340654.
%Y A340651 A007716 counts non-isomorphic multiset partitions.
%Y A340651 A007718 counts non-isomorphic connected multiset partitions.
%Y A340651 A316980 counts non-isomorphic strict multiset partitions.
%Y A340651 Other balance-related sequences:
%Y A340651 - A047993 counts balanced partitions.
%Y A340651 - A106529 lists balanced numbers.
%Y A340651 - A340596 counts co-balanced factorizations.
%Y A340651 - A340599 counts alt-balanced factorizations.
%Y A340651 - A340600 counts unlabeled balanced multiset partitions.
%Y A340651 - A340653 counts balanced factorizations.
%Y A340651 Cf. A001055, A007717, A064174, A316983, A320663, A324522, A339888, A340655.
%K A340651 nonn
%O A340651 0,3
%A A340651 _Gus Wiseman_, Feb 05 2021
%E A340651 a(11) onwards from _Andrew Howroyd_, Jan 15 2024