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%I #6 Apr 07 2013 02:43:50
%S 357,112311,2540727,28861191,239301927,1663126311,10343555367,
%T 59654395431,325892779047,1709482140711,8689254356007,43074112914471,
%U 209214647804967,999137244521511,4704103526212647,21880432615990311,100713104634651687,459359353571484711
%N The hyper-Wiener index of the dendrimer D_3[n], defined pictorially in the A. R. Ashrafi et al. reference.
%C a(0) and a(1) have 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) = 107559 - 551400*2^n + 108900*4^n*n^2 + 444198*4^n -304590*4^n*n + 74910*2^n*n - 18150*2^n*n^2.
%F G.f. = 3(119+35176z+153456z^2-931008z^3+391824z^4+1360960z^5-42496z^6)/[(1-z)(1-2z)^3(1-4z)^3].
%p a := proc (n) options operator, arrow: 107559-551400*2^n + 108900*4^n*n^2 + 444198*4^n - 304590*4^n*n + 74910*2^n*n - 18150*2^n*n^2 end proc: seq(a(n), n = 0 .. 17);
%Y Cf. A224433
%K nonn
%O 0,1
%A _Emeric Deutsch_, Apr 06 2013
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