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 A158448 a(n) equals the number of admissible pairs of subsets of {1,2,...,n} in the notation of Marzuola-Miller. 1
 1, 2, 3, 8, 18, 50, 135, 385, 1065, 3053, 8701, 25579, 73693, 217718, 635220, 1888802 (list; graph; refs; listen; history; text; internal format)
 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,...} REFERENCES J. Marzuola, A. Miller, "Counting numerical sets with no small atoms", to appear in Journal of Combinatorial Theory: A. LINKS 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.uni-bonn.de), Aug 08 2009 Edited by R. J. Mathar, Aug 31 2009 STATUS approved

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