A192839 Molecular topological indices of the square graphs.

0, 48, 768, 4320, 15360, 42000, 96768, 197568, 368640, 641520, 1056000, 1661088, 2515968, 3690960, 5268480, 7344000, 10027008, 13441968, 17729280, 23046240, 29568000, 37488528, 47021568, 58401600, 71884800, 87750000, 106299648, 127860768, 152785920, 181454160

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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) = 8*n*(n+1)*(n-1)^3.

G.f.: 48*x^2*(1+x)*(1+9*x)/(1-x)^6. - Colin Barker, Aug 07 2012

E.g.f.: 8*x^2*(3 + 13*x + 8*x^2 + x^3)*exp(x). - G. C. Greubel, Jan 04 2019

From Amiram Eldar, Apr 16 2022: (Start)

Sum_{n>=2} 1/a(n) = 13/128 - Pi^2/64 + zeta(3)/16.

Sum_{n>=2} (-1)^n/a(n) = log(2)/4 - Pi^2/128 - 17/128 + 3*zeta(3)/64. (End)

Maple

[8*n*(n+1)*(n-1)^3$n=1..30]; # Muniru A Asiru, Jan 05 2019

Mathematica

Table[, {n, 1, 30}] (* G. C. Greubel, Jan 04 2019 *)

Prog

(PARI) vector(30, n, 8*n*(n+1)*(n-1)^3) \\ G. C. Greubel, Jan 04 2019
(Magma) [8*n*(n+1)*(n-1)^3: n in [1..30]]; // G. C. Greubel, Jan 04 2019
(Sage) [8*n*(n+1)*(n-1)^3 for n in (1..30)] # G. C. Greubel, Jan 04 2019
(GAP) List([1..30], n -> 8*n*(n+1)*(n-1)^3); # G. C. Greubel, Jan 04 2019

Crossrefs

Sequence in context: A145155 A105948 A350378 * A014401 A241873 A233784

Adjacent sequences: A192836 A192837 A192838 * A192840 A192841 A192842

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 11 2011

Status

approved