

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,...}


REFERENCES

J. Marzuola, A. Miller, "Counting numerical sets with no small atoms", to appear in Journal of Combinatorial Theory: A.


LINKS

Table of n, a(n) for n=1..16.
S. R. Finch, Monoids of natural numbers
J. Marzuola and A. Miller, Counting numerical sets with no small atoms, arXiv:0805.3493.


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: A002369 A005957 A185171 * A073192 A113183 A157015
Adjacent sequences: A158445 A158446 A158447 * A158449 A158450 A158451


KEYWORD

nonn


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



