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

1,2

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).

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

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A334713 A266210 A245953 * A352847 A042949 A190601

Adjacent sequences: A192829 A192830 A192831 * A192833 A192834 A192835

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 11 2011

Status

approved