A216107 The hyper-Wiener index of the tetrameric 1,3-adamantane TA(n) (see the Fath-Tabar et al. reference).

168, 1720, 6636, 17796, 38980, 74868, 131040, 213976, 331056, 490560, 701668, 974460, 1319916, 1749916, 2277240, 2915568, 3679480, 4584456, 5646876, 6884020, 8314068, 9956100, 11830096, 13956936, 16358400, 19057168, 22076820, 25441836, 29177596, 33310380

Offset

1,1

Comments

The Hosoya-Wiener polynomial of TA(n) is n(10+12t+18t^2+12t^3+3t^4)+(1+3t+3t^2+3t^3)^2*(t^{3n+1}-nt^4+nt-1)/(t^3-1)^2.

Links

Table of n, a(n) for n=1..30.

G. H. Fath-Tabar, A. Azad, and N. Elahinezhad, Some topological indices of tetrameric 1,3-adamantane, Iranian J. Math. Chemistry, 1, No. 1, 2010, 111-118.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = (75n^4 +210n^3 + 229n^2-178n)/2.

G.f.: -4*x*(34*x^3-71*x^2+220*x+42)/(x-1)^5. [Colin Barker, Oct 31 2012]

Maple

seq((75*n^4+210*n^3+229*n^2-178*n)*(1/2), n=1..30);

Mathematica

Table[(75n^4+210n^3+229n^2-178n)/2, {n, 30}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {168, 1720, 6636, 17796, 38980}, 30] (* Harvey P. Dale, Jan 01 2016 *)

Crossrefs

Cf. A216106.

Sequence in context: A112551 A303622 A263121 * A235932 A235926 A279725

Adjacent sequences: A216104 A216105 A216106 * A216108 A216109 A216110

Keyword

nonn,easy

Author

Emeric Deutsch, Oct 26 2012

Status

approved