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A192828 Molecular topological indices of the n X n grid graphs 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 04:11 EST 2021. Contains 340443 sequences. (Running on oeis4.)