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Molecular topological indices of the complete bipartite graphs K_{n,n}.
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%I #65 Oct 30 2019 01:29:46

%S 4,48,180,448,900,1584,2548,3840,5508,7600,10164,13248,16900,21168,

%T 26100,31744,38148,45360,53428,62400,72324,83248,95220,108288,122500,

%U 137904,154548,172480,191748,212400

%N Molecular topological indices of the complete bipartite graphs K_{n,n}.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteBipartiteGraph.html">Complete Bipartite Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MolecularTopologicalIndex.html">Molecular Topological Index</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n) = 4*n^2*(2*n-1).

%F a(n) = 4*A015237(n).

%F G.f.: 4*x*(3*x^2+8*x+1)/(x-1)^4. - _Colin Barker_, Nov 04 2012

%F a(n) = 2*n * A002939(n). - _Bruce J. Nicholson_, Oct 14 2019

%F E.g.f.: 4*exp(x)*x*(1 + 5*x + 2*x^2). - _Stefano Spezia_, Oct 15 2019

%t Table[4n^2(2n-1),{n,30}] (* or *) LinearRecurrence[{4,-6,4,-1},{4,48,180,448},30] (* _Harvey P. Dale_, Apr 08 2018 *)

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Jul 10 2011