A227711 - OEIS

%I #18 Sep 08 2022 08:46:05

%S 403929,7123491,73556943,584118615,3973793223,24439248231,

%T 140086159911,762624306855,3992164666791,20266876319655,

%U 100389136655271,487362872044455,2326764524198823,10952675858742183,50938660677696423,234448450914335655,1069296992883227559

%N The hyper-Wiener index of the nanostar dendrimer defined pictorially in Fig. 2 of the Madanshekaf reference.

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

%D A. Madanshekaf, The Randic index of some dendrimer nanostars, J. Appl. Math. & Informatics, 29, 2011, 1075-1080.

%H Vincenzo Librandi, <a href="/A227711/b227711.txt">Table of n, a(n) for n = 1..300</a>

%F a(n) = 4^n*(254016*n^2-728028*n+1207116) + 2^n*(13104*n^2-50682*n-1250685)+48039.

%F G.f.: 3*x*(134643-183720*x-400012*x^2-612832*x^3+2889984*x^4 -2158592*x^5 +762880*x^6)/((1-x)*(1-2*x)^3*(1-4*x)^3).

%p a := proc (n) options operator, arrow: 4^n*(254016*n^2-728028*n+1207116) +2^n*(13104*n^2-50682*n-1250685)+48039 end proc: seq(a(n), n = 1 .. 20);

%t CoefficientList[Series[3 (134643 - 183720 x - 400012 x^2 - 612832 x^3 + 2889984 x^4 - 2158592 x^5 + 762880 x^6) / ((1 - x) (1 - 2 x)^3 (1 - 4 x)^3), {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 05 2013 *)

%o (Magma) [4^n*(254016*n^2-728028*n+1207116)+2^n*(13104*n^2-50682*n-1250685)+48039: n in [1..20]]; // _Vincenzo Librandi_, Aug 04 2013

%Y Cf. A227710.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, Aug 03 2013

%E Typo in the g.f. corrected from _Bruno Berselli_, Aug 05 2013