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%I #20 Sep 08 2022 08:45:58
%S 0,48,576,2880,9600,25200,56448,112896,207360,356400,580800,906048,
%T 1362816,1987440,2822400,3916800,5326848,7116336,9357120,12129600,
%U 15523200,19636848,24579456,30470400,37440000,45630000,55194048,66298176,79121280,93855600
%N Molecular topological indices of the lattice graphs.
%C Lattice graphs are defined for n>=2; extended to n=1 using closed form.
%H G. C. Greubel, <a href="/A192832/b192832.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LatticeGraph.html">Lattice 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_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(n) = 4*n^2*(n+1)*(n-1)^2.
%F a(n) = 48*A004302(n).
%F G.f.: 48*x^2*(1+6*x+3*x^2)/(1-x)^6. - _Colin Barker_, Aug 07 2012
%F E.g.f.: 4*x^2*(6 +18*x +9*x^2 +x^3)*exp(x). - _G. C. Greubel_, Jan 04 2019
%t Table[4*n^2*(n+1)*(n-1)^2, {n,1,30}] (* _G. C. Greubel_, Jan 04 2019 *)
%o (PARI) vector(30, n, 4*n^2*(n+1)*(n-1)^2) \\ _G. C. Greubel_, Jan 04 2019
%o (Magma) [4*n^2*(n+1)*(n-1)^2: n in [1..30]]; // _G. C. Greubel_, Jan 04 2019
%o (Sage) [4*n^2*(n+1)*(n-1)^2 for n in (1..30)] # _G. C. Greubel_, Jan 04 2019
%o (GAP) List([0..30], n -> 4*n^2*(n+1)*(n-1)^2); # _G. C. Greubel_, Jan 04 2019
%K nonn,easy
%O 1,2
%A _Eric W. Weisstein_, Jul 11 2011
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