A122658 a(n) = if n mod 2 = 1 then n^3*(n-1)^2/2 else n^5/2.

0, 0, 16, 54, 512, 1000, 3888, 6174, 16384, 23328, 50000, 66550, 124416, 158184, 268912, 330750, 524288, 628864, 944784, 1111158, 1600000, 1852200, 2576816, 2944414, 3981312, 4500000, 5940688, 6652854, 8605184, 9560488, 12150000, 13405950, 16777216, 18399744

Offset: 0

Author

N. J. A. Sloane, Sep 22 2006

Keywords

• nonn
• easy

Comments

Szeged index of product of two cycles of length n.

Links

• Janez Žerovnik, Szeged index of symmetric graphs, J. Chem. Inf. Comput. Sci., 39 (1999), 77-80; alternative link.
• Index entries for linear recurrences with constant coefficients, signature (1,5,-5,-10,10,10,-10,-5,5,1,-1).

Crossrefs

Cf. A002117, A013661, A013663, A122656.

Programs

Mathematica

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 *)

Formula

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

Sum_{n>=2} 1/a(n) = zeta(5)/16 + 7*zeta(3)/4 + 7*zeta(2)/2 + 6*log(2) - 12. - Amiram Eldar, May 15 2024