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A228307 The hyper-Wiener index of the Kneser graph K(n,2) (n>=5).

%I A228307 #10 Feb 16 2025 08:33:20
%S A228307 105,225,420,714,1134,1710,2475,3465,4719,6279,8190,10500,13260,16524,
%T A228307 20349,24795,29925,35805,42504,50094,58650,68250,78975,90909,104139,
%U A228307 118755,134850,152520,171864,192984,215985,240975,268065,297369,329004,363090
%N A228307 The hyper-Wiener index of the Kneser graph K(n,2) (n>=5).
%C A228307 The Kneser graph K(n,2) is the graph whose vertices represent the 2-subsets of {1,2,...,n} and two vertices are connected if and only if they correspond to disjoint subsets.
%C A228307 K(n,2) is disconnected for n<=4.
%C A228307 K(5,2) is the Petersen graph.
%C A228307 The Kneser graph K(n,2) is distance-regular with intersection array [(n-2)*(n-3)/2, 2*(n-4); 1, (n-3)*(n-4)/2].
%D A228307 R. Balakkrishnan, S. Francis Raj, The Wiener number of Kneser graphs, Discussiones Math, Graph Theory, 28, 2008, 219-228.
%H A228307 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KneserGraph.html">Kneser Graph</a>.
%H A228307 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A228307 a(n) = (1/8)*n*(n-1)*(n-2)*(n+9).
%F A228307 G.f.: 3*x^5*(35-100*x+115*x^2-62*x^3+13*x^4)/(1-x)^5.
%F A228307 The Hosoya-Wiener polynomial of K(n,2) is (1/8)*n*(n-1)*(n-2)*t*(n-3+4*t).
%F A228307 a(n) = 3*A095661(n-3). - _R. J. Mathar_, Aug 21 2013
%p A228307 a := proc (n) options operator, arrow: (1/8)*n*(n-1)*(n-2)*(n+9) end proc: seq(a(n), n = 5 .. 40);
%Y A228307 Cf. A228306
%K A228307 nonn,easy
%O A228307 5,1
%A A228307 _Emeric Deutsch_, Aug 20 2013