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%I #33 Apr 16 2021 21:58:09
%S 19,71,181,379,701,1189,1891,2861,4159,5851,8009,10711,14041,18089,
%T 22951,28729,35531,43471,52669,63251,75349,89101,104651,122149,141751,
%U 163619,187921,214831,244529,277201,313039,352241,395011,441559,492101,546859,606061,669941,738739,812701,892079
%N Number of wedged n-spheres in the homotopy type of the neighborhood complex of Kneser graph KG_{3,n}.
%C 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.
%H Nandini Nilakantan and Anurag Singh, <a href="https://arxiv.org/abs/1807.11732">Neighborhood complexes of Kneser graphs KG_{3,k}</a>, arXiv:1807.11732 [math.CO], 2018.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = 1 + (n+1)*(n+3)*(n+4)*(n+6)/4.
%F G.f.: (19 - 24* x + 16*x^2 - 6*x^3 + x^4)/(1 - x)^5. - _Stefano Spezia_, Mar 22 2021
%e 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.
%o (Sage) [1+((n+1)*(n+3)*(n+4)*(n+6)/4) for n in range(50)]
%K nonn,easy
%O 0,1
%A _Anurag Singh_, Mar 21 2021
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