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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 *) PROG (PARI) a(n)=2*n*(1+2*n+2*n^2) \\ Charles R Greathouse IV, Oct 18 2022 CROSSREFS Cf. A227704. Sequence in context: A044303 A044684 A346882 * A044384 A044765 A297627 Adjacent sequences: A227700 A227701 A227702 * A227704 A227705 A227706 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jul 25 2013 STATUS approved

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Last modified April 14 07:36 EDT 2024. Contains 371655 sequences. (Running on oeis4.)