Number of subsets with at least 3 elements of an n-element set.
For n>4, number of simple rank-(n-1) matroids over S_n.
Number of non-interval subsets of {1,2,3,...,n} (cf.
A000124). - Jose Luis Arregui (arregui(AT)unizar.es), Jun 27 2006
a(n) is the number of binary sequences of length n having at least three 0's. -
Geoffrey Critzer, Feb 11 2009
Starting with "1" = eigensequence of a triangle with the tetrahedral numbers (1, 4, 10, 20, ...) as the left border and the rest 1's. -
Gary W. Adamson, Jul 24 2010
a(n) is also the number of crossing set partitions of [n+1] with two blocks. -
Peter Luschny, Apr 29 2011
Nonzero terms of this sequence can be found from the row sums of the fourth sub-triangle extracted from Pascal's triangle as indicated below by braces:
1;
1, 1;
1, 2, 1;
{1}, 3, 3, 1;
{1, 4}, 6, 4, 1;
{1, 5, 10}, 10, 5, 1;
{1, 6, 15, 20}, 15, 6, 1;
... (End)
Partial sums of
A000295 (Eulerian Numbers, Column 2).
Starting (0, 0, 1, 5, 16, ...) is the binomial transform of (0, 0, 1, 2, 2, 2, ...). -
Gary W. Adamson, Jul 27 2015
a(n - 1) is the rank of the divisor class group of the moduli space of stable rational curves with n marked points, see Keel p. 550. -
Harry Richman, Aug 10 2024
a(n) is the number of binary strings of length n that contain at least two runs of ones. -
Félix Balado, Sep 16 2025
