A227487 - OEIS

%I #11 Jun 23 2023 07:48:46

%S 34255,398665,3470157,25438869,166187685,999925445,5660148997,

%T 30581012869,159315487365,806202248325,3984535138437,19312921409669,

%U 92094055975045,433117479708805,2012917990713477,9259384642267269,42212038923118725,190920673305290885,857470623117994117,3827025150533953669

%N The hyper-Wiener index of the nanostar dendrimer defined pictorially as G[n] in the M. H. Khalifeh et al. reference.

%C a(0) and a(1) have been checked by the direct computation of the Wiener index (using Maple).

%H M. K. Khalifeh, H. Yousefi-Azari, and A. R. Ashrafi, <a href="https://chalcogen.ro/1Khalifeh.pdf">The Szeged and Wiener numbers of water soluble polyaryl ether dendrimer nanostars</a>, Digest J. Nanomaterials and Biostructures, 4, 2009, 63-66.

%F a(n) = -6011+2^n*(-111166-5960*n+7000*n^2)+4^n*(151432-35200*n+40000*n^2).

%F G.f.: (34255 -252180*z + 1033772*z^2 -2480544*z^3+3259584*z^4-2547712*z^5+790528*z^6)/((1-z)*(1-2*z)^3*(1-4*z)^3).

%p a := proc (n) options operator, arrow: -6011+2^n*(-111166-5960*n+7000*n^2)+4^n*(151432-35200*n+40000*n^2) end proc: seq(a(n), n = 0 .. 20);

%Y Cf. A227486

%K nonn

%O 0,1

%A _Emeric Deutsch_, Jul 13 2013