The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A122658 a(n) = if n mod 2 = 1 then n^3*(n-1)^2/2 else n^5/2. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
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).
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
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 *)
CROSSREFS
Sequence in context: A167690 A297842 A172190 * A224040 A244805 A362039
KEYWORD
nonn,easy,changed
AUTHOR
N. J. A. Sloane, Sep 22 2006
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 24 03:29 EDT 2024. Contains 372771 sequences. (Running on oeis4.)