A221005 - OEIS

%I #9 Jun 23 2023 10:51:59

%S 4797,18800,88530,500582,3112014,19362974,115754814,659875454,

%T 3602117886,18956429822,96789115902,482029987838,2351490682878,

%U 11274381991934,53269435990014,248554431348734,1147271095058430,5245861041405950,23788748016975870,107088865925791742,478941290597187582

%N The hyper-Wiener index of the nanostar dendrimer NS[n], defined pictorially in the Wang-Hua reference.

%H H. Wang and H. Hua, <a href="https://chalcogen.ro/497_Wang.pdf">Computing the second- and third- connectivity index of an infinite class of dendrimer nanostars</a>, Digest J. Nanomaterials and Biostructures, 5 (2010) 497-502.

%H L. Yang and H. Hua, <a href="https://oam-rc.inoe.ro/articles/modified-terminal-wiener-index-of-a-type-of-dendrimer-nanostars/fulltext">Modified terminal Wiener index of a type of dendrimer nanostars</a>, Optoelectronics and Advanced Materials - Rapid Communications, 5 (2011) 160-163.

%F a(n) = -2+2^n*(1404*n^2+1764*n-3115)+4^n*(1296*n^2-4536*n+7914).

%F G.f.: (4797-72343*x+450880*x^2-1412380*x^3+2406976*x^4-2246848*x^5+868864*x^6)/((1-x)*(1-2*x)^3*(1-4*x)^3). - _Bruno Berselli_, Dec 30 2012

%p a := proc (n) options operator, arrow: -2+2^n*(1404*n^2+1764*n-3115)+4^n*(1296*n^2-4536*n+7914) end proc: seq(a(n), n = 0 .. 20);

%Y Cf. A221004.

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, Dec 29 2012