A227708 - OEIS

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

%S 84,354,1674,8178,39858,191250,900498,4164114,18952722,85106706,

%T 377862162,1661755410,7249502226,31410683922,135299432466,

%U 579837493266,2473936945170,10514155438098,44530379784210,188016821796882,791649070350354

%N The 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="/A227708/b227708.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (13,-64,148,-160,64).

%F a(n) = 18 + 2^n*(66+30*n) + 36*n*4^n.

%F G.f.: 6*(14-123*x+408*x^2-560*x^3+288*x^4)/((1-x)*(1-2*x)^2*(1-4*x)^2).

%F a(0)=84, a(1)=354, a(2)=1674, a(3)=8178, a(4)=39858, a(n)=13*a(n-1)- 64*a(n-2)+ 148*a(n-3)- 160*a(n-4)+64*a(n-5). - _Harvey P. Dale_, Jan 09 2016

%p a := proc (n) options operator, arrow: 18+2^n*(66+30*n)+36*4^n*n end proc: seq(a(n), n = 0 .. 25);

%t CoefficientList[Series[6 (14 - 123 x + 408 x^2 - 560 x^3 + 288 x^4) / ((1 - x) (1 - 2 x)^2 (1 - 4 x)^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 04 2013 *)

%t LinearRecurrence[{13,-64,148,-160,64},{84,354,1674,8178,39858},30] (* _Harvey P. Dale_, Jan 09 2016 *)

%o (Magma) [18+2^n*(66+30*n)+36*n*4^n: n in [0..25]]; // _Vincenzo Librandi_, Aug 04 2013

%Y Cf. A227707, A227709.

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, Aug 02 2013

%E Typo in formula fixed by _Vincenzo Librandi_, Aug 04 2013