A192418 Molecular topological indices of the complete bipartite graphs K_{n,n}.

4, 48, 180, 448, 900, 1584, 2548, 3840, 5508, 7600, 10164, 13248, 16900, 21168, 26100, 31744, 38148, 45360, 53428, 62400, 72324, 83248, 95220, 108288, 122500, 137904, 154548, 172480, 191748, 212400

Offset: 1

Author

Eric W. Weisstein, Jul 10 2011

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, Complete Bipartite Graph
• Eric Weisstein's World of Mathematics, Molecular Topological Index
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

Mathematica

Table[4n^2(2n-1),{n,30}] (* or *) LinearRecurrence[{4,-6,4,-1},{4,48,180,448},30] (* Harvey P. Dale, Apr 08 2018 *)

Formula

a(n) = 4*n^2*(2*n-1).

a(n) = 4*A015237(n).

G.f.: 4*x*(3*x^2+8*x+1)/(x-1)^4. - Colin Barker, Nov 04 2012

a(n) = 2*n * A002939(n). - Bruce J. Nicholson, Oct 14 2019

E.g.f.: 4*exp(x)*x*(1 + 5*x + 2*x^2). - Stefano Spezia, Oct 15 2019