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 A228306 The Wiener index of the Kneser graph K(n,2) (n>=5). 1
 75, 165, 315, 546, 882, 1350, 1980, 2805, 3861, 5187, 6825, 8820, 11220, 14076, 17442, 21375, 25935, 31185, 37191, 44022, 51750, 60450, 70200, 81081, 93177, 106575, 121365, 137640, 155496, 175032, 196350, 219555, 244755, 272061, 301587, 333450 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,1 COMMENTS 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. K(n,2) is disconnected for n<=4. K(5,2) is the Petersen graph. 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]. REFERENCES R. Balakkrishnan, S. Francis Raj, The Wiener number of Kneser graphs, Discussiones Math, Graph Theory, 28, 2008, 219-228. LINKS Table of n, a(n) for n=5..40. Eric Weisstein's World of Mathematics, Kneser Graph. Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = (1/8)*n*(n-1)*(n-2)*(n+5). G.f.: 3*x^5*(25-70*x+80*x^2-43*x^3+9*x^4)/(1-x)^5. The Hosoya-Wiener polynomial of K(n,2) is (1/8)*n*(n-1)*(n-2)*t*(n-3+4*t). MAPLE a := proc (n) options operator, arrow: (1/8)*n*(n-1)*(n-2)*(n+5) end proc: seq(a(n), n = 5 .. 40); CROSSREFS Cf. A228307 Sequence in context: A023095 A044326 A044707 * A044407 A044788 A003503 Adjacent sequences: A228303 A228304 A228305 * A228307 A228308 A228309 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Aug 20 2013 STATUS approved

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Last modified June 10 11:14 EDT 2023. Contains 363200 sequences. (Running on oeis4.)