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

2,1

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).

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

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 *)

Prog

(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
(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
(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
(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

Crossrefs

Sequence in context: A281374 A190416 A231342 * A259851 A223419 A333671

Adjacent sequences: A192825 A192826 A192827 * A192829 A192830 A192831

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 11 2011

Status

approved