A342737 Number of wedged n-spheres in the homotopy type of the neighborhood complex of Kneser graph KG_{3,n}.

19, 71, 181, 379, 701, 1189, 1891, 2861, 4159, 5851, 8009, 10711, 14041, 18089, 22951, 28729, 35531, 43471, 52669, 63251, 75349, 89101, 104651, 122149, 141751, 163619, 187921, 214831, 244529, 277201, 313039, 352241, 395011, 441559, 492101, 546859, 606061, 669941, 738739, 812701, 892079

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

Table of n, a(n) for n=0..40.

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

Sequence in context: A198002 A093350 A226802 * A142516 A127874 A289817

Adjacent sequences: A342734 A342735 A342736 * A342738 A342739 A342740

Keyword

nonn,easy

Author

Anurag Singh, Mar 21 2021

Status

approved