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A227703 The Wiener index of the zig-zag polyhex nanotube TUHC_6[2n,2] defined pictorially in Fig. 1 of the Eliasi et al. reference. 2
52, 150, 328, 610, 1020, 1582, 2320, 3258, 4420, 5830, 7512, 9490, 11788, 14430, 17440, 20842, 24660, 28918, 33640, 38850, 44572, 50830, 57648, 65050, 73060, 81702, 91000, 100978, 111660, 123070, 135232, 148170, 161908, 176470, 191880 (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 Wiener index (using Maple).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 2..1000

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 (4,-6,4,-1).

FORMULA

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

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

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: 2*n*(1+2*n+2*n^2) end proc: seq(a(n), n = 2 .. 40);

MATHEMATICA

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 *)

CROSSREFS

Cf. A227704

Sequence in context: A044303 A044684 A346882 * A044384 A044765 A297627

Adjacent sequences:  A227700 A227701 A227702 * A227704 A227705 A227706

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Jul 25 2013

STATUS

approved

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Last modified October 22 22:35 EDT 2021. Contains 348180 sequences. (Running on oeis4.)