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%I #14 Mar 26 2024 10:29:19
%S 1,2,3,6,17,43,109,278,708,1803,4592,11695,29785,75857,193194,492030,
%T 1253111,3191446,8128033,20700623,52720725,134270106,341961560,
%U 870913951,2218059568,5648994647,14386962813,36640979841,93317917142
%N a(1)=1; a(2)=2; a(3)=3; a(n) = Sum_{k=3..n-1} (a(k) + a(k-1) + a(k-2)).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,1).
%F a(n) is asymptotic to a*b^n where a = 0.1570450524507584150437292... and b is the real root of: x^3 - 2*x^2 - x - 1; b = 2.546818276884082079135997..
%F a(n) = 2*a(n-1)+a(n-2)+a(n-3) for n>4. G.f.: x*(3*x^3+2*x^2-1) / (x^3+x^2+2*x-1). - _Colin Barker_, Jun 24 2013
%K nonn,easy
%O 1,2
%A _Benoit Cloitre_, Nov 22 2002
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