OFFSET
0,1
COMMENTS
KG_{3,n} is a graph whose vertex set is the collection of subsets of cardinality 3 of set {1,2,...,n+5,n+6} and two subsets are adjacent if and only if they are disjoint. For n >= 0, the neighborhood complex of KG_{3,n} is homotopy equivalent to a wedge of 1 + (n+1)*(n+3)*(n+4)*(n+6)/4 spheres of dimension n.
LINKS
Nandini Nilakantan and Anurag Singh, Neighborhood complexes of Kneser graphs KG_{3,k}, arXiv:1807.11732 [math.CO], 2018.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = 1 + (n+1)*(n+3)*(n+4)*(n+6)/4.
G.f.: (19 - 24* x + 16*x^2 - 6*x^3 + x^4)/(1 - x)^5. - Stefano Spezia, Mar 22 2021
EXAMPLE
a(0)=19 because the neighborhood complex of KG_{3,0} is the vertex set of KG_{3,0}, which is a wedge of 19 spheres of dimension 0. Observe that KG_{3,0} has 20 vertices and 10 edges.
PROG
(Sage) [1+((n+1)*(n+3)*(n+4)*(n+6)/4) for n in range(50)]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Anurag Singh, Mar 21 2021
STATUS
approved