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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.
2
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, 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, 2, 6
OFFSET
1,30
COMMENTS
Caps of a clutter are defined in the link, and the generalization to "multiclutters," where edges can be multisets, is straightforward.
LINKS
Gus Wiseman, Every Clutter Is a Tree of Blobs, The Mathematica Journal, Vol. 19, 2017.
EXAMPLE
The a(30) = 2 z-blobs together with the corresponding multiset systems:
(30): {{1,2,3}}
(18,12): {{1,2,2},{1,1,2}}
The a(47) = 3 z-blobs together with the corresponding multiset systems:
(47): {{15}}
(21,14,12): {{2,4},{1,4},{1,1,2}}
(20,15,12): {{1,1,3},{2,3},{1,1,2}}
The a(60) = 5 z-blobs together with the corresponding multiset systems:
(60): {{1,1,2,3}}
(42,18): {{1,2,4},{1,2,2}}
(36,24): {{1,1,2,2},{1,1,1,2}}
(30,18,12): {{1,2,3},{1,2,2},{1,1,2}}
(21,15,14,10): {{2,4},{2,3},{1,4},{1,3}}
The a(67) = 7 z-blobs together with the corresponding multiset systems:
(67): {{19}}
(45,12,10): {{2,2,3},{1,1,2},{1,3}}
(42,15,10): {{1,2,4},{2,3},{1,3}}
(40,15,12): {{1,1,1,3},{2,3},{1,1,2}}
(33,22,12): {{2,5},{1,5},{1,1,2}}
(28,21,18): {{1,1,4},{2,4},{1,2,2}}
(24,18,15,10): {{1,1,1,2},{1,2,2},{2,3},{1,3}}
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 27 2018
STATUS
approved