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

0,3

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).

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

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 *)

Crossrefs

Cf. A034828, A122658.

Sequence in context: A085540 A259546 A355553 * A152692 A351845 A037966

Adjacent sequences: A122654 A122655 A122656 * A122658 A122659 A122660

Keyword

nonn

Author

N. J. A. Sloane, Sep 22 2006

Status

approved