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