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A192828 Molecular topological indices of the n X n grid graphs.

%I A192828 #22 Jul 22 2025 12:16:31
%S A192828 48,440,2008,6468,16736,37248,74280,136268,234128,381576,595448,
%T A192828 896020,1307328,1857488,2579016,3509148,4690160,6169688,8001048,
%U A192828 10243556,12962848,16231200,20127848,24739308,30159696,36491048,43843640,52336308,62096768
%N A192828 Molecular topological indices of the n X n grid graphs.
%H A192828 G. C. Greubel, <a href="/A192828/b192828.txt">Table of n, a(n) for n = 2..1000</a>
%H A192828 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%H A192828 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MolecularTopologicalIndex.html">Molecular Topological Index</a>
%H A192828 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A192828 a(n) = 2*(2+n)*(6 -24*n +25*n^2 -13*n^3 +4*n^4)/3.
%F A192828 G.f.: 4*x^2*(12+38*x+22*x^2+15*x^3-8*x^4+x^5)/(1-x)^6. - _Colin Barker_, Aug 07 2012
%F A192828 E.g.f.: 2*(-12 +6*x + (12 -18*x +48*x^2 +69*x^3 +35*x^4 +4*x^5)*exp(x) )/3. - _G. C. Greubel_, Jan 03 2019
%t A192828 Table[2*(2+n)*(6-24*n+25*n^2-13*n^3+4*n^4)/3, {n,2,40}] (* _G. C. Greubel_, Jan 03 2019 *)
%o A192828 (PARI) {a(n) = 2*(2+n)*(6-24*n+25*n^2-13*n^3+4*n^4)/3}; \\ _G. C. Greubel_, Jan 03 2019
%o A192828 (Magma) [2*(2+n)*(6-24*n+25*n^2-13*n^3+4*n^4)/3: n in [2..40]]; // _G. C. Greubel_, Jan 03 2019
%o A192828 (Sage) [2*(2+n)*(6-24*n+25*n^2-13*n^3+4*n^4)/3 for n in (2..40)] # _G. C. Greubel_, Jan 03 2019
%o A192828 (GAP) List([2..40], n -> 2*(2+n)*(6-24*n+25*n^2-13*n^3+4*n^4)/3); # _G. C. Greubel_, Jan 03 2019
%K A192828 nonn,easy
%O A192828 2,1
%A A192828 _Eric W. Weisstein_, Jul 11 2011