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%I #8 Jul 22 2022 11:31:44
%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.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (19,-150,636,-1560,2208,-1664,512).
%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,easy
%O 0,1
%A _Emeric Deutsch_, Apr 06 2013
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