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%I #10 Nov 20 2016 15:06:11
%S 0,0,16,54,512,1000,3888,6174,16384,23328,50000,66550,124416,158184,
%T 268912,330750,524288,628864,944784,1111158,1600000,1852200,2576816,
%U 2944414,3981312,4500000,5940688,6652854,8605184,9560488,12150000,13405950,16777216,18399744
%N a(n) = if n mod 2 = 1 then n^3*(n-1)^2/2 else n^5/2.
%C Szeged index of product of two cycles of length n.
%D J. Zerovnik, Szeged index of symmetric graphs, J. Chem. Inf. Comput. Sci., 39 (1999), 77-80.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,-5,-10,10,10,-10,-5,5,1,-1).
%F a(n) = (n^3*(1-(-1)^n+2*(-1+(-1)^n)*n+2*n^2))/4. G.f.: 2*x^2*(x^8 +7*x^7 +95*x^6 +113*x^5 +379*x^4 +149*x^3 +189*x^2 +19*x +8) / ((x -1)^6*(x +1)^5). - _Colin Barker_, Sep 20 2013
%t Table[If[OddQ[n],n^3 (n-1)^2/2,n^5/2],{n,0,40}] (* or *) LinearRecurrence[ {1,5,-5,-10,10,10,-10,-5,5,1,-1},{0,0,16,54,512,1000,3888,6174,16384,23328,50000},40] (* _Harvey P. Dale_, Nov 20 2016 *)
%Y Cf. A122656.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Sep 22 2006
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