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A224430 The hyper-Wiener index of the dendrimer D_1[n], defined pictorially in the A. R. Ashrafi et al. reference. 1

%I

%S 159,104448,2123802,22761810,183445458,1256801106,7758199698,

%T 44564150802,242917046802,1272665857554,6464520301074,32033885569554,

%U 155562155893266,742852590887442,3497424488243730,16268164668891666,74884202558956050,341573770043761170,1545606217427624466

%N The hyper-Wiener index of the dendrimer D_1[n], defined pictorially in the A. R. Ashrafi et al. reference.

%C a(2) has been checked by the direct computation of the hyper-Wiener index (using Maple).

%D A. R. Ashrafi and H. Shabani, Computing Padmakar-Ivan index of four classes of dendrimers, Bulgarian Chem. Comm., 44, N0. 2, 2012, 127-130.

%F a(n) = 41490 - 420000*2^n + 81225*4^n*n^2 - 467115*4^n*n/2 + 378669*4^n + 231*2^n*n - 1425*2^n*n^2.

%F G.f. = 3(53+33809z+54380z^2-674784z^3+1120160z^4-847120z^5+686912z^6)/[(1-z)(1-2z)^3*(1-4z)^3].

%p a := proc (n) options operator, arrow: 41490-420000*2^n+81225*4^n*n^2-(467115/2)*4^n*n+378669*4^n+231*2^n*n-1425*2^n*n^2 end proc: seq(a(n), n = 0 .. 18);

%Y Cf. A224429

%K nonn

%O 0,1

%A _Emeric Deutsch_, Apr 06 2013

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Last modified June 30 19:12 EDT 2022. Contains 354945 sequences. (Running on oeis4.)