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A224455
The hyper-Wiener index of the linear phenylene with n hexagons.
3
42, 396, 1656, 4740, 10890, 21672, 38976, 65016, 102330, 153780, 222552, 312156, 426426, 569520, 745920, 960432, 1218186, 1524636, 1885560, 2307060, 2795562, 3357816, 4000896, 4732200, 5559450, 6490692, 7534296, 8698956, 9993690, 11427840, 13011072, 14753376, 16665066, 18756780, 21039480
OFFSET
1,1
COMMENTS
a(2) and a(5) have been checked by the direct computation of the hyper-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) = (3/2)*n*(n+1)*(9*n^2 + 3*n + 2).
G.f.: 6*x*(7 + 31*x + 16*x^2)/(1-x)^5.
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) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - G. C. Greubel, Dec 08 2016
MAPLE
a := proc (n) options operator, arrow: (3/2)*n*(n+1)*(9*n^2+3*n+2) end proc: seq(a(n), n = 1 .. 35);
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {42, 396, 1656, 4740, 10890}, 100] (* or *) Table[(3/2)*n*(n+1)*(9*n^2 + 3*n + 2), {n, 1, 100}] (* G. C. Greubel, Dec 08 2016 *)
PROG
(PARI) Vec(6*x*(7 + 31*x + 16*x^2)/(1-x)^5 + O(x^50)) \\ G. C. Greubel, Dec 08 2016
CROSSREFS
Cf. A224454.
Sequence in context: A189496 A064302 A231705 * A114928 A364943 A127545
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Apr 10 2013
STATUS
approved