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%I A084080 #6 Mar 30 2012 18:58:50
%S A084080 1,1,1,2,3,4,9,15,22,52,91,140,340,612,969,2394,4389,7084,17710,32890,
%T A084080 53820,135720,254475,420732,1068012,2017356,3362260,8579560,16301164,
%U A084080 27343888,70068713
%N A084080 Length of lists created by n substitutions k -> Range[k+1,1,-3] starting with {1}, counting down from k+1 to 1 step -3.
%C A084080 Would appear to coincide with row sums of the inverse of the Riordan array (1-x^3,x(1-x^3)). These row sums have g.f. 1/(1-y-y^3+y^4) where y^4-y+x=0. - _Paul Barry_, May 10 2005
%e A084080 {1}, {2}, {3}, {4, 1}, {5, 2, 2}, {6, 3, 3, 3}, {7, 4, 1, 4, 1, 4, 1, 4, 1}
%t A084080 Length/@Flatten/@NestList[ # /. k_Integer:>Range[k+1, 1, -3]&, {1}, 21]
%Y A084080 Cf. A124753.
%K A084080 nonn
%O A084080 0,4
%A A084080 _Wouter Meeussen_, May 11 2003

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