A227703 - OEIS

%I #14 Oct 18 2022 15:09:35

%S 52,150,328,610,1020,1582,2320,3258,4420,5830,7512,9490,11788,14430,

%T 17440,20842,24660,28918,33640,38850,44572,50830,57648,65050,73060,

%U 81702,91000,100978,111660,123070,135232,148170,161908,176470,191880

%N The Wiener index of the zig-zag polyhex nanotube TUHC_6[2n,2] defined pictorially in Fig. 1 of the Eliasi et al. reference.

%C a(2), a(3), ..., a(6) have been checked by the direct computation of the Wiener index (using Maple).

%H Harvey P. Dale, <a href="/A227703/b227703.txt">Table of n, a(n) for n = 2..1000</a>

%H M. Eliasi, A. Iranmanesh, <a href="https://doi.org/10.1016/j.dam.2010.12.020">The hyper-Wiener index of the generalized hierarchical product of graphs</a>, Discrete Appl. Math., 159, 2011, 866-871.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n) = 2*n*(1 + 2*n + 2*n^2).

%F G.f. = 2*x^2*(26-29*x+20*x^2-5*x^3)/(1-x)^4.

%F The Hosoya-Wiener polynomial of TUHC_6[2n,2] is n*(2*t^n*(1 + t)^2 + t^4 - t^3 - 3*t^2 - 5*t)/(t - 1).

%p a := proc (n) options operator, arrow: 2*n*(1+2*n+2*n^2) end proc: seq(a(n), n = 2 .. 40);

%t Table[2n(1+2n+2n^2),{n,2,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{52,150,328,610},40] (* _Harvey P. Dale_, Jan 15 2015 *)

%o (PARI) a(n)=2*n*(1+2*n+2*n^2) \\ _Charles R Greathouse IV_, Oct 18 2022

%Y Cf. A227704.

%K nonn,easy

%O 2,1

%A _Emeric Deutsch_, Jul 25 2013