0,4

a(n) is the absolute value of the reduced Euler characteristic for the simplicial complex of bipartite (2-colorable) graphs on n+1 vertices. - Jakob Jonsson (jonsson(AT)mathematik.uni-marburg.de), Apr 03 2003

F(x) = -sqrt(2*exp(-x)-1)+1 is the exponential generating function for the sequence shifted one step (0,1,0,1,3,16,105,...). The first derivative of F coincides with the generating function in the name line. F aligns better with the given Euler characteristic as the coefficient of x^n corresponds to graphs on n vertices (rather than n+1 vertices). - Jakob Jonsson (jonsson(AT)mathematik.uni-marburg.de), Apr 03 2003

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Exercise 5.5.

S. Linusson and J. Shareshian, Complexes of t-colorable graphs.

a(3) = 3 because the following graphs are bipartite on four vertices: The empty graph (1 graph); all graphs with one edge (6 graphs); all graphs with two edges (15 graphs); graphs with three edges not forming a triangle (16 graphs); and graphs with four edges forming a square (3 graphs). The reduced Euler characteristic is hence -1 + 6 - 15 + 16 - 3 = 3. - Jakob Jonsson (jonsson(AT)mathematik.uni-marburg.de), Apr 03 2003

Sequence in context: A105622 A110903 A085614 this_sequence A063548 A157452 A074551

Adjacent sequences: A014301 A014302 A014303 this_sequence A014305 A014306 A014307

nonn

N. J. A. Sloane (njas(AT)research.att.com).