A122656 a(n) = n*floor(n/2)^2.

0, 0, 2, 3, 16, 20, 54, 63, 128, 144, 250, 275, 432, 468, 686, 735, 1024, 1088, 1458, 1539, 2000, 2100, 2662, 2783, 3456, 3600, 4394, 4563, 5488, 5684, 6750, 6975, 8192, 8448, 9826, 10115, 11664, 11988, 13718, 14079, 16000, 16400, 18522, 18963, 21296, 21780

Offset: 0

Author

N. J. A. Sloane, Sep 22 2006

Keywords

• nonn
• easy

Comments

Szeged index of cycle of length n.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• 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 (1,3,-3,-3,3,1,-1).

Crossrefs

Cf. A002117, A013661, A008794.

Programs

Magma

[n*Floor(n/2)^2: n in [0..50]]; // Vincenzo Librandi, May 31 2014

Mathematica

Table[n Floor[n/2]^2,{n,0,50}] (* or *) LinearRecurrence[ {1,3,-3,-3,3,1,-1},{0,0,2,3,16,20,54},50] (* Harvey P. Dale, May 31 2014 *)

Formula

a(n) = (n*(1-(-1)^n+2*(-1+(-1)^n)*n+2*n^2))/8. G.f.: x^2*(x^4+x^3+7*x^2+x+2) / ((x-1)^4*(x+1)^3). - Colin Barker, Sep 20 2013

a(n) = n*A008794(n). - R. J. Mathar, Mar 04 2018

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