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%I #30 Sep 08 2022 08:45:58
%S 0,4,80,800,6248,43424,283880,1793600,11110088,68008544,413290280,
%T 2500208000,15081582728,90806120864,546088834280,3281497784000,
%U 19708713860168,118330793948384,710297609395880,4263033439001600,25583180948198408,153518974465539104
%N Molecular topological indices of the Mycielski graphs.
%H Colin Barker, <a href="/A192834/b192834.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MolecularTopologicalIndex.html">Molecular Topological Index</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MycielskiGraph.html">Mycielski Graph</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (16,-95,260,-324,144).
%F a(n) = (3*2^n - 8)*(18 - 27*2^n + 14*3^n)/36, n > 1, with a(1)=0.
%F G.f.: 4*x^2*(12*x^4 - 2*x^3 + 25*x^2 - 4*x - 1)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(6*x-1)). - _Colin Barker_, Aug 07 2012
%F E.g.f.: (25 + 12*x - 144*exp(x) + 270*exp(2*x) - 112*exp(3*x) - 81*exp(4*x) + 42*exp(6*x))/36. - _G. C. Greubel_, Jan 04 2019
%p 0,seq((3*2^n-8)*(18-27*2^n+14*3^n)/36,n=2..25); # _Muniru A Asiru_, Jan 05 2019
%t Table[If[n==1, 0, (3*2^n-8)*(18-27*2^n+14*3^n)/36], {n,1,30}]
%o (PARI) concat(0, Vec(4*x^2*(12*x^4-2*x^3+25*x^2-4*x-1)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(6*x-1)) + O(x^30))) \\ _Colin Barker_, Oct 14 2017
%o (PARI) vector(30, n, if(n==1,0,(3*2^n-8)*(18-27*2^n+14*3^n)/36)) \\ _G. C. Greubel_, Jan 04 2019
%o (Magma) [0] cat [(3*2^n-8)*(18-27*2^n+14*3^n)/36: n in [2..30]]; // _G. C. Greubel_, Jan 04 2019
%o (Sage) [0] + [(3*2^n-8)*(18-27*2^n+14*3^n)/36 for n in (2..30)] # _G. C. Greubel_, Jan 04 2019
%o (GAP) Concatenation([0], List([2..30], n -> (3*2^n-8)*(18-27*2^n+ 14*3^n)/36)); # _G. C. Greubel_, Jan 04 2019
%Y Cf. A122695.
%K nonn,easy
%O 1,2
%A _Eric W. Weisstein_, Jul 11 2011
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