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
Examples
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.
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).
Extensions
Definition rephrased by Jeremy L. Marzuola (marzuola(AT)math.uni-bonn.de), Aug 08 2009
Edited by R. J. Mathar, Aug 31 2009
Comments