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

%I #18 Nov 12 2016 12:21:40

%S 168,1720,6636,17796,38980,74868,131040,213976,331056,490560,701668,

%T 974460,1319916,1749916,2277240,2915568,3679480,4584456,5646876,

%U 6884020,8314068,9956100,11830096,13956936,16358400,19057168,22076820,25441836,29177596,33310380

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

%C 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.

%H G. H. Fath-Tabar, A. Azad, and N. Elahinezhad, <a href="http://en.journals.sid.ir/ViewPaper.aspx?ID=254060">Some topological indices of tetrameric 1,3-adamantane</a>, Iranian J. Math. Chemistry, 1, No. 1, 2010, 111-118.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

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

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

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

%t 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 *)

%Y Cf. A216106.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, Oct 26 2012

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)