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%I #5 Mar 31 2012 13:21:13
%S 0,1,2,1,3,2,2,1,2,4,3,3,2,3,3,2,2,1,2,3,2,3,2,5,4,4,3,4,4,3,3,2,3,4,
%T 3,4,3,4,3,3,2,3,3,2,2,1,2,3,2,3,2,4,3,3,2,3,4,3,4,3,3,2,3,2,3,6,5,5,
%U 4,5,5,4,4,3,4,5,4,5,4,5,4,4,3,4,4,3,3,2,3,4,3,4,3,5,4,4,3,4,5,4,5,4
%N a(n) = number of nodes with odd distance to the root in the n-th plane general tree encoded by A014486(n). Both internal and terminal nodes (leaves) are counted.
%e A014486(27) = 696 (1010111000 in binary), encodes the following general plane tree, where the root is marked with * and nodes with even or odd distance to root with 'e's and 'o's, respectively.
%e .......o
%e .......|
%e .......e
%e .......|
%e ...o.o.o
%e ....\|/.
%e .....*..
%e there are four nodes marked with 'o', thus a(27)=4.
%o (MIT Scheme:) (define (A126303 n) (*A126303 (A014486->parenthesization (A014486 n))))
%o (define (*A126303 s) (cond ((null? s) 0) (else (fold-left (lambda (x y) (+ x 1 (*A126304 y))) 0 s))))
%Y a(n) = A072643(n)-A126305(n). Cf. A126304. Scheme-function A014486->parenthesization given in A014486.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jan 02 2007
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