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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 26 23:44 EDT 2022. Contains 357051 sequences. (Running on oeis4.)