A192828 Molecular topological indices of the n X n grid graphs.

48, 440, 2008, 6468, 16736, 37248, 74280, 136268, 234128, 381576, 595448, 896020, 1307328, 1857488, 2579016, 3509148, 4690160, 6169688, 8001048, 10243556, 12962848, 16231200, 20127848, 24739308, 30159696, 36491048, 43843640, 52336308, 62096768

Offset: 2

Author

Eric W. Weisstein, Jul 11 2011

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000
• Eric Weisstein's World of Mathematics, Grid 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([2..40], n -> 2*(2+n)*(6-24*n+25*n^2-13*n^3+4*n^4)/3); # G. C. Greubel, Jan 03 2019

Magma

[2*(2+n)*(6-24*n+25*n^2-13*n^3+4*n^4)/3: n in [2..40]]; // G. C. Greubel, Jan 03 2019

Mathematica

Table[2*(2+n)*(6-24*n+25*n^2-13*n^3+4*n^4)/3, {n,2,40}] (* G. C. Greubel, Jan 03 2019 *)

PARI

{a(n) = 2*(2+n)*(6-24*n+25*n^2-13*n^3+4*n^4)/3}; \\ G. C. Greubel, Jan 03 2019

Sage

[2*(2+n)*(6-24*n+25*n^2-13*n^3+4*n^4)/3 for n in (2..40)] # G. C. Greubel, Jan 03 2019

Formula

a(n) = 2*(2+n)*(6 -24*n +25*n^2 -13*n^3 +4*n^4)/3.

G.f.: 4*x^2*(12+38*x+22*x^2+15*x^3-8*x^4+x^5)/(1-x)^6. - Colin Barker, Aug 07 2012

E.g.f.: 2*(-12 +6*x + (12 -18*x +48*x^2 +69*x^3 +35*x^4 +4*x^5)*exp(x) )/3. - G. C. Greubel, Jan 03 2019