A158448 a(n) equals the number of admissible pairs of subsets of {1,2,...,n} in the notation of Marzuola-Miller.

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

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

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) 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

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.uni-bonn.de), Aug 08 2009

Edited by R. J. Mathar, Aug 31 2009

Status

approved