A224429 - OEIS

%I #13 Feb 11 2025 18:47:24

%S 84,18327,233565,1771209,10839249,59193537,301745505,1470068769,

%T 6938902689,32002414497,145020899745,648175476129,2865160922529,

%U 12550658135457,54563037754785,235694448080289,1012548295652769,4329277751424417,18433454242526625

%N The Wiener index of the dendrimer D_1[n], defined pictorially in the A. R. Ashrafi et al. reference.

%C a(2) has been checked by the direct computation of the Wiener index (using Maple).

%D A. R. Ashrafi and H. Shabani, Computing Padmakar-Ivan index of four classes of dendrimers, Bulgarian Chem. Comm., 44, N0. 2, 2012, 127-130.

%H Harvey P. Dale, <a href="/A224429/b224429.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) = - 2655 + 26907*2^n + 16245*n*4^n -24168*4^n -570*n*2^n.

%F G.f. = 3(28+5745z+230z^2-34880z^3+20912z^4)/[(1-z)(1-2z)^2*(1-4z)^2].

%p a := proc (n) options operator, arrow: -2655+26907*2^n+16245*4^n*n-24168*4^n-570*2^n*n end proc: seq(a(n), n = 0 .. 18);

%t LinearRecurrence[{13,-64,148,-160,64},{84,18327,233565,1771209,10839249},20] (* _Harvey P. Dale_, Feb 11 2025 *)

%Y Cf. A224430

%K nonn,easy,changed

%O 0,1

%A _Emeric Deutsch_, Apr 06 2013