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A221006 The Wiener index of the nanostar dendrimer NS[n], defined pictorially in the Karbasioun-Ashrafi-Diudea reference. 1

%I #15 Feb 13 2024 08:15:52

%S 1296,14526,107082,649890,3539538,18027954,87813234,414505458,

%T 1911928050,8665131762,38733797106,171235454706,750157258482,

%U 3261519544050,14089697722098,60533384085234,258832139157234,1102123427954418,4675674117242610,19771419930918642,83360577251966706

%N The Wiener index of the nanostar dendrimer NS[n], defined pictorially in the Karbasioun-Ashrafi-Diudea reference.

%H A. Karbasioun, A. R. Ashrafi, and M. V. Diudea, <a href="https://match.pmf.kg.ac.rs/electronic_versions/Match63/n1/match63n1_239-246.pdf">Distance and detour matrices of an infinite class of dendrimer nanostars</a>, MATCH Commun. Math. Comput. Chem. 63, 2010, 239-246.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (11,-42,64,-32).

%F a(n) = -270 + 2^n*3510+4^n*(3888*n-1944) (see Theorem 1 in the Karbasioun-Ashrafi-Diudea reference).

%F G.f.: -54*(16*x^3-32*x^2-5*x-24) / ((x-1)*(2*x-1)*(4*x-1)^2). [_Colin Barker_, Jan 01 2013]

%p a := proc (n) options operator, arrow: -270+3510*2^n+4^n*(3888*n-1944) end proc: seq(a(n), n = 0 .. 20);

%Y Cf. A221007.

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, Dec 29 2012

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Last modified July 19 01:31 EDT 2024. Contains 374388 sequences. (Running on oeis4.)