%I #28 Oct 05 2019 04:55:51

%S 2,8,16,48,192,384,1152,4608,9216,27648,110592,221184,663552,2654208,

%T 5308416,15925248,63700992,127401984,382205952,1528823808,3057647616,

%U 9172942848,36691771392,73383542784,220150628352,880602513408

%N Expansion of 2*x*(1+4*x+8*x^2)/(1-24*x^3).

%C Previous name was: 3 people at a party are saying Hello to each other. Person 2 says Hello Hello. Person 3 counts the times Hello has been said and says Hello thrice that number of times. Person 1 says Hello a number of times equal to the sum of Hello's and then it is Person 2's turn again. This is the total number of Hello's said.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,24).

%F G.f.: 2*x*(1+4*x+8*x^2)/(1-24*x^3). - _Colin Barker_, Jun 07 2012

%F a(n) = 2^n*b(n-1) where b(n) = 1, 2, 2, 3, 6, 6, 9, 18, 18, 27, 54, ... (n >= 0) is A038754 with each 2nd term repeated. - _R. J. Mathar_, May 21 2018

%Y Partial sums of A076507.

%K nonn,easy

%O 1,1

%A _Jon Perry_, Oct 15 2002