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A224454
The Wiener index of the linear phenylene with n hexagons.
3
27, 180, 567, 1296, 2475, 4212, 6615, 9792, 13851, 18900, 25047, 32400, 41067, 51156, 62775, 76032, 91035, 107892, 126711, 147600, 170667, 196020, 223767, 254016, 286875, 322452, 360855, 402192, 446571, 494100, 544887, 599040, 656667, 717876, 782775, 851472, 924075, 1000692, 1081431, 1166400
OFFSET
1,1
COMMENTS
a(2) and a(5) have been checked by the direct computation of the Wiener index (using Maple).
REFERENCES
I. Gutman, The topological indices of linear phenylenes, J. Serb. Chem. Soc., 60, No. 2, 1995, 99-104.
LINKS
G. Cash, S. Klavzar, M. Petkovsek, Three methods for calculation of the hyper-Wiener index of a molecular graph, J. Chem. Inf. Comput. Sci. 42, 2002, 571-576.
L. Pavlovic, I. Gutman, Wiener numbers of phenylenes: an exact result, J. Chem. Inf. Comput. Sci. 37, 1997, 355-358.
FORMULA
a(n) = 9*n^2*(2n+1) = 9*A099721(n).
G.f.: 9*x*(3 + 8*x + x^2)/(1-x)^4.
The Hosoya polynomial of the linear phenylene with n hexagons is nt(t^3-t^2-4t-8)/(t-1) + 2t(t+1)(t^(3n)-1)/(t-1)^2.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - G. C. Greubel, Dec 08 2016
MAPLE
a := proc (n) options operator, arrow: 9*n^2*(2*n+1) end proc: seq(a(n), n = 1 .. 40);
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {27, 180, 567, 1296}, 100] (* or *) Table[9*n^2*(2*n+1), {n, 1, 100}] (* G. C. Greubel, Dec 08 2016 *)
PROG
(PARI) Vec(9*x*(3 + 8*x + x^2)/(1-x)^4 + O(x^50)) \\ G. C. Greubel, Dec 08 2016
(Magma) [9*n^2*(2*n+1): n in [1..40]]; // Vincenzo Librandi, Dec 09 2016
CROSSREFS
Cf. A224455.
Sequence in context: A083560 A125337 A126495 * A258637 A228463 A000499
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Apr 10 2013
STATUS
approved