A227704 The hyper-Wiener index of the zig-zag polyhex nanotube TUHC_6[2n,2] defined pictorially in Fig. 1 of the Eliasi et al. reference.

82, 273, 692, 1475, 2790, 4837, 7848, 12087, 17850, 25465, 35292, 47723, 63182, 82125, 105040, 132447, 164898, 202977, 247300, 298515, 357302, 424373, 500472, 586375, 682890, 790857, 911148, 1044667, 1192350, 1355165, 1534112, 1730223

Offset

2,1

Comments

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

Links

Table of n, a(n) for n=2..33.

M. Eliasi, A. Iranmanesh, The hyper-Wiener index of the generalized hierarchical product of graphs, Discrete Appl. Math., 159, 2011, 866-871.

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

Formula

a(n) = n*(15 + 14*n + 12*n^2 + 4*n^3)/3 (see Example 1 in the Eliasi et al. reference).

G.f. = x^2*(82-137*x+147*x^2-75*x^3+15*x^4)/(1-x)^5.

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).

Maple

a := proc (n) options operator, arrow: (1/3)*n*(15+14*n+12*n^2+4*n^3) end proc: seq(a(n), n = 2 .. 35);

Crossrefs

Cf. A227703.

Sequence in context: A317268 A258739 A048513 * A248405 A116341 A102956

Adjacent sequences: A227701 A227702 A227703 * A227705 A227706 A227707

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 25 2013

Status

approved