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%I #22 Oct 05 2019 04:55:06
%S 3,6,18,72,144,432,1728,3456,10368,41472,82944,248832,995328,1990656,
%T 5971968,23887872,47775744,143327232,573308928,1146617856,3439853568,
%U 13759414272,27518828544,82556485632,330225942528,660451885056
%N Expansion of 3*(1+2*x+6 x^2)/(1-24*x^3).
%C Previous name was: 3 people at a party are saying Hello to each other. Person 3 says Hello Hello Hello. Person 1 counts the times Hello has been said and says Hello that number of times. Person 2 says Hello a number of times equal to 2 * the sum of Hello's said; then it is Person 3's turn again. Sequence gives 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 From _Harvey P. Dale_, Jul 23 2011: (Start)
%F a(0)=3, a(1)=6, a(2)=18, a(n)=24*a(n-3).
%F G.f.: 3*(1+2*x+6 x^2)/(1-24*x^3). (End)
%t LinearRecurrence[{0,0,24},{3,6,18},50] (* _Harvey P. Dale_, Jul 23 2011 *)
%Y Cf. A076509.
%K nonn
%O 1,1
%A _Jon Perry_, Oct 15 2002
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