A122657 a(n) = if n mod 2 = 1 then (n^2-1)*n^3/4 else n^5/4.

0, 0, 8, 54, 256, 750, 1944, 4116, 8192, 14580, 25000, 39930, 62208, 92274, 134456, 189000, 262144, 353736, 472392, 617310, 800000, 1018710, 1288408, 1606044, 1990656, 2437500, 2970344, 3582306, 4302592, 5121690, 6075000, 7149840, 8388608, 9774864, 11358856

Offset: 0

Author

N. J. A. Sloane, Sep 22 2006

Keywords

• nonn

Comments

Wiener index of product of two cycles of length n.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Torus Grid Graph
• Eric Weisstein's World of Mathematics, Wiener Index
• J. Zerovnik, Szeged index of symmetric graphs, J. Chem. Inf. Comput. Sci., 39 (1999), 77-80.
• Index entries for linear recurrences with constant coefficients, signature (2,3,-8,-2,12,-2,-8,3,2,-1).

Crossrefs

Cf. A034828, A122658.

Programs

Mathematica

Table[If[Mod[n, 2] == 0, n^5, (n^2 - 1) n^3]/4, {n, 0, 20}] (* Eric W. Weisstein, May 10 2017 *)
LinearRecurrence[{2, 3, -8, -2, 12, -2, -8, 3, 2, -1}, {0, 8, 54, 256,
   750, 1944, 4116, 8192, 14580, 25000}, {0, 20}] (* Eric W. Weisstein, May 10 2017 *)
CoefficientList[Series[2 x^2 (4 x^6 + 19 x^5 + 62 x^4 + 70 x^3 + 62 x^2 + 19 x + 4)/((x + 1)^4 (x - 1)^6), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 08 2017 *)
If[OddQ[#],((#^2-1)#^3)/4,#^5/4]&/@Range[0,40] (* Harvey P. Dale, Jul 03 2021 *)

Formula

G.f.: 2*x^2*(4*x^6+19*x^5+62*x^4+70*x^3+62*x^2+19*x+4) /((x+1)^4*(x-1)^6). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009