OFFSET
1,2
COMMENTS
Alternate description: a(n) is the number of vertices at height n in the rooted tree in figure 4 of [Marzuola-Miller] which spawn only three vertices at height n+1.
The number of numerical sets S with atom monoid A(S) equal to {0,n+1, 2n+2,2n+3,2n+4,2n+5,...}
LINKS
S. R. Finch, Monoids of natural numbers
S. R. Finch, Monoids of natural numbers, March 17, 2009. [Cached copy, with permission of the author]
J. Marzuola and A. Miller, Counting numerical sets with no small atoms, arXiv:0805.3493 [math.CO], 2008.
J. Marzuola and A. Miller, Counting numerical sets with no small atoms, J. Combin. Theory A 117 (6) (2010) 650-667.
FORMULA
Recursively related to A164048 (call it A'()) by the formula A(2k+1)' = 2A(2k)'-a(k).
EXAMPLE
a(3)=3 since {0,4,8,9,10,11,...}, {0,1,4,5,8,9,10,11,...} and {0,1,2, 4,5,6,8,9,10,11,...} are the only three sets satisfying the required conditions.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Steven Finch, Mar 19 2009
EXTENSIONS
Definition rephrased by Jeremy L. Marzuola (marzuola(AT)math.uni-bonn.de), Aug 08 2009
Edited by R. J. Mathar, Aug 31 2009
STATUS
approved