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A224456 The Wiener index of the cyclic phenylene with n hexagons (n>=3). 1

%I #10 Mar 29 2019 04:06:49

%S 459,1008,1845,3024,4599,6624,9153,12240,15939,20304,25389,31248,

%T 37935,45504,54009,63504,74043,85680,98469,112464,127719,144288,

%U 162225,181584,202419,224784,248733,274320,301599,330624,361449,394128,428715,465264,503829,544464,587223,632160

%N The Wiener index of the cyclic phenylene with n hexagons (n>=3).

%C a(3), a(4), ... , a(16) have been checked by the direct computation of the Wiener index (using Maple).

%D Y. Alizadeh, S. Klavzar, The Wiener dimension of a graph (unpublished manuscript).

%H G. Cash, S. Klavzar, M. Petkovsek, <a href="https://doi.org/10.1021/ci0100999">Three methods for calculation of the hyper-Wiener index of a molecular graph</a>, J. Chem. Inf. Comput. Sci. 42, 2002, 571-576.

%F a(n) = 9n(n^2+4n-4).

%F G.f.: 9z^3(51-92z+63z^2-16z^3)/(1-z)^4.

%F The Hosoya polynomial of the cyclic phenylene with n hexagons is [n*t^n*(t^5+3t^4+5t^3+5t^2+3t+1) - n(t^8+t^7+t^6+t^5+2t^3+4t^2+8t)]/(t-1).

%p a := proc (n) options operator, arrow: 9*n*(n^2+4*n-4) end proc: seq(a(n), n = 3 .. 40);

%Y Cf. A224457.

%K nonn

%O 3,1

%A _Emeric Deutsch_, Apr 14 2013

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)