A057119 Iterative "rewrite" sequence of binary plane trees.
2, 10, 180, 47940, 3185189700, 13760582141553025860, 254536428082497193743150874618461037380, 86730091025558229301371439971941296450524845723997443510460490068605668041540
Offset: 0
Keywords
Examples
We start from the simplest such binary tree: 0.0 (binary depth-first encoding = 2, from left to right, 1 with the zero of the last leaf ignored); then encode it as an ordinary rooted plane tree (depth-first-wise) to get the code 1010 = decimal 10, which in turn, when interpreted as an encoding of binary tree is: ..0.0 .0.1. (whose rooted plane tree coding is 10110100 = 180 in decimal) ..1.. etc.
Programs
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Maple
a(n) = bt_df2tree_apply_k_times(2,n) bt_df2tree_apply_k_times := proc(n,k) option remember; if(0 = k) then (n) else bt_df2tree_apply_k_times(bintree_depth_first2tree(n),k-1); fi; end; bintree_depth_first2tree := n -> ((btdf2t(n*2,floor_log_2(n)+1)/2) - 2^(2*(floor_log_2(n)+1))); btdf2t := proc(n,ii) local i,e,x,y; i := ii; if(n >= (2^i)) then x := btdf2t(n - (2^i),i-1); i := i - ((floor_log_2(x)+1)/2); y := btdf2t((n mod (2^i)),i-1); RETURN((2^(floor_log_2(y)+2))*((2^(floor_log_2(x)+1)) + x) + 2*y); else RETURN(2); fi; end;
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