cp's OEIS Frontend

A305195 Number of z-blobs summing to n. Number of connected strict integer partitions of n, with pairwise indivisible parts, that cannot be capped by a z-tree.

%I A305195 #7 Jul 15 2018 13:23:33
%S A305195 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,
%T A305195 1,1,2,1,1,1,3,3,2,1,1,1,3,2,2,2,1,1,3,3,3,1,1,1,4,5,6,2,1,1,4,6,7,2,
%U A305195 2,6
%N A305195 Number of z-blobs summing to n. Number of connected strict integer partitions of n, with pairwise indivisible parts, that cannot be capped by a z-tree.
%C A305195 Caps of a clutter are defined in the link, and the generalization to "multiclutters," where edges can be multisets, is straightforward.
%H A305195 Gus Wiseman, <a href="http://www.mathematica-journal.com/2017/12/every-clutter-is-a-tree-of-blobs/">Every Clutter Is a Tree of Blobs</a>, The Mathematica Journal, Vol. 19, 2017.
%e A305195 The a(30) = 2 z-blobs together with the corresponding multiset systems:
%e A305195      (30): {{1,2,3}}
%e A305195   (18,12): {{1,2,2},{1,1,2}}
%e A305195 The a(47) = 3 z-blobs together with the corresponding multiset systems:
%e A305195         (47): {{15}}
%e A305195   (21,14,12): {{2,4},{1,4},{1,1,2}}
%e A305195   (20,15,12): {{1,1,3},{2,3},{1,1,2}}
%e A305195 The a(60) = 5 z-blobs together with the corresponding multiset systems:
%e A305195            (60): {{1,1,2,3}}
%e A305195         (42,18): {{1,2,4},{1,2,2}}
%e A305195         (36,24): {{1,1,2,2},{1,1,1,2}}
%e A305195      (30,18,12): {{1,2,3},{1,2,2},{1,1,2}}
%e A305195   (21,15,14,10): {{2,4},{2,3},{1,4},{1,3}}
%e A305195 The a(67) = 7 z-blobs together with the corresponding multiset systems:
%e A305195            (67): {{19}}
%e A305195      (45,12,10): {{2,2,3},{1,1,2},{1,3}}
%e A305195      (42,15,10): {{1,2,4},{2,3},{1,3}}
%e A305195      (40,15,12): {{1,1,1,3},{2,3},{1,1,2}}
%e A305195      (33,22,12): {{2,5},{1,5},{1,1,2}}
%e A305195      (28,21,18): {{1,1,4},{2,4},{1,2,2}}
%e A305195   (24,18,15,10): {{1,1,1,2},{1,2,2},{2,3},{1,3}}
%Y A305195 Cf. A030019, A048143, A275307, A285572, A293510, A303362, A303837, A303838, A304118, A304382, A304887, A305028, A305078, A305194.
%K A305195 nonn
%O A305195 1,30
%A A305195 _Gus Wiseman_, May 27 2018