

A158448


a(n) equals the number of admissible pairs of subsets of {1,2,...,n} in the notation of MarzuolaMiller.


1



1, 2, 3, 8, 18, 50, 135, 385, 1065, 3053, 8701, 25579, 73693, 217718, 635220, 1888802
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OFFSET

1,2


COMMENTS

Alternate description: a(n) is the number of vertices at height n in the rooted tree in figure 4 of [MarzuolaMiller] 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

Table of n, a(n) for n=1..16.
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) 650667.


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

Cf. A158291, A164048.
Sequence in context: A005957 A185171 A339524 * A073192 A317722 A113183
Adjacent sequences: A158445 A158446 A158447 * A158449 A158450 A158451


KEYWORD

nonn,more


AUTHOR

Steven Finch, Mar 19 2009


EXTENSIONS

Definition rephrased by Jeremy L. Marzuola (marzuola(AT)math.unibonn.de), Aug 08 2009
Edited by R. J. Mathar, Aug 31 2009


STATUS

approved



