A126303 - OEIS

%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