%I #11 Sep 08 2022 08:46:05

%S 159,906,5664,34932,206652,1168620,6344268,33264780,169424652,

%T 842319372,4104041484,19659270156,92822679564,432877854732,

%U 1997218529292,9129086189580,41386604691468,186264812126220,832881548328972,3702608701685772,16373934411743244

%N The hyper-Wiener index of the dendrimer D_n defined pictorially in Fig. 1 of the Heydari et al. reference.

%C a(2) has been checked by the direct computation of the distance matrix (with Maple).

%D A. Heydari, I. Gutman, On the terminal index of thorn graphs, Kragujevac J. Sci., 32, 2010, 57-64.

%H Vincenzo Librandi, <a href="/A227709/b227709.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = 12+2^n*(15+45*n+15*n^2) + 4^n*(132+18*n+36*n^2).

%F G.f.: 3*(53-705*x+4100*x^2-12636*x^3+21456*x^4-19328*x^5+7168*x^6)/((1-x)*(1-2*x)^3*(1-4*x)^3).

%p a := proc (n) options operator, arrow: 12+2^n*(15+45*n+15*n^2)+4^n*(132+18*n+36*n^2) end proc: seq(a(n), n = 0 .. 23);

%t CoefficientList[Series[3 (53 - 705 x + 4100 x^2 - 12636 x^3 + 21456 x^4 - 19328 x^5 + 7168 x^6) / ((1 - x) (1 - 2 x)^3 (1 - 4 x)^3), {x, 0, 25}], x] (* _Vincenzo Librandi_, Aug 04 2013 *)

%o (Magma) [12+2^n*(15+45*n+15*n^2)+4^n*(132+18*n+36*n^2): n in [0..25]]; // _Vincenzo Librandi_, Aug 04 2013

%Y Cf. A227707, A227708.

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, Aug 02 2013