A192832 Molecular topological indices of the lattice graphs.

0, 48, 576, 2880, 9600, 25200, 56448, 112896, 207360, 356400, 580800, 906048, 1362816, 1987440, 2822400, 3916800, 5326848, 7116336, 9357120, 12129600, 15523200, 19636848, 24579456, 30470400, 37440000, 45630000, 55194048, 66298176, 79121280, 93855600

Offset: 1

Author

Eric W. Weisstein, Jul 11 2011

Keywords

• nonn
• easy

Comments

Lattice graphs are defined for n>=2; extended to n=1 using closed form.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Lattice Graph
• Eric Weisstein's World of Mathematics, Molecular Topological Index
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Programs

GAP

List([0..30], n -> 4*n^2*(n+1)*(n-1)^2); # G. C. Greubel, Jan 04 2019

Magma

[4*n^2*(n+1)*(n-1)^2: n in [1..30]]; // G. C. Greubel, Jan 04 2019

Mathematica

Table[4*n^2*(n+1)*(n-1)^2, {n,1,30}] (* G. C. Greubel, Jan 04 2019 *)

PARI

vector(30, n, 4*n^2*(n+1)*(n-1)^2) \\ G. C. Greubel, Jan 04 2019

Sage

[4*n^2*(n+1)*(n-1)^2 for n in (1..30)] # G. C. Greubel, Jan 04 2019

Formula

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

a(n) = 48*A004302(n).

G.f.: 48*x^2*(1+6*x+3*x^2)/(1-x)^6. - Colin Barker, Aug 07 2012

E.g.f.: 4*x^2*(6 +18*x +9*x^2 +x^3)*exp(x). - G. C. Greubel, Jan 04 2019