A192829 Molecular topological indices of the n X n X n grid graphs.

360, 8064, 68928, 355470, 1340424, 4086180, 10680384, 24847938, 52769640, 104137704, 193478400, 341772054, 578400648, 943453260, 1490419584, 2289301770, 3430174824, 5027225808, 7223302080, 10194998814, 14158316040, 19374915444, 26159007168, 34884896850, 45995223144, 60009915960, 77535905664, 99277613478, 126048253320

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 (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = n*(24-66*n+36*n^2+4*n^3-3*n^4-7*n^5+6*n^6).

G.f.: 6*x^2*(60+864*x+2416*x^2+1613*x^3+44*x^4+50*x^5-8*x^6+x^7)/(1-x)^8. - Colin Barker, Aug 07 2012

E.g.f.: x*(6 +(-6 +186*x +1161*x^2 +1619*x^3 +732*x^4 +119*x^5+6*x^6)* exp(x)). - G. C. Greubel, Jan 04 2019

Mathematica

Table[n*(24-66*n+36*n^2+4*n^3-3*n^4-7*n^5+6*n^6), {n, 2, 40}] (* G. C. Greubel, Jan 04 2019 *)

Prog

(PARI) vector(40, n, n++; n*(24-66*n+36*n^2+4*n^3-3*n^4-7*n^5+6*n^6)) \\ G. C. Greubel, Jan 04 2019
(Magma) [n*(24-66*n+36*n^2+4*n^3-3*n^4-7*n^5+6*n^6): n in [2..40]]; // G. C. Greubel, Jan 04 2019
(Sage) [n*(24-66*n+36*n^2+4*n^3-3*n^4-7*n^5+6*n^6) for n in (2..40)] # G. C. Greubel, Jan 04 2019
(GAP) List([2..40], n -> n*(24-66*n+36*n^2+4*n^3-3*n^4-7*n^5+6*n^6)); # G. C. Greubel, Jan 04 2019

Crossrefs

Sequence in context: A305626 A056322 A056313 * A229681 A054648 A230684

Adjacent sequences: A192826 A192827 A192828 * A192830 A192831 A192832

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 11 2011

Status

approved