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Molecular topological indices of the complete tripartite graphs K_{n,n,n}.
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%I #29 May 31 2022 13:20:12

%S 24,240,864,2112,4200,7344,11760,17664,25272,34800,46464,60480,77064,

%T 96432,118800,144384,173400,206064,242592,283200,328104,377520,431664,

%U 490752,555000,624624,699840,780864,867912,961200

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteTripartiteGraph.html">Complete Tripartite 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) = 12*n^2*(3*n-1).

%F a(n) = 24*A050509(n).

%F G.f.: 24*x*(2*x^2+6*x+1)/(x-1)^4. [_Colin Barker_, Nov 04 2012]

%F From _Bruce J. Nicholson_, Sep 18 2019: (Start)

%F a(n) = 24*n * A000326(n).

%F a(n) = 4*n^2 * A017233(n).

%F a(n) = 24*(n^3 + A000292(n-2) + A000330(n-2)).

%F a(n) = 24*(n^4 - (A008585(n) * A000330(n-1))).

%F a(n) = 6*A046092(n) + (A008594(n+1) * A140676(n-1)). (End)

%Y Cf. A000326, A000330, A000292, A017233, A008594, A140676, A046092.

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Jul 10 2011