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