A126304 - OEIS

%I #5 Mar 31 2012 13:21:13

%S 0,0,0,1,0,1,1,2,1,0,1,1,2,1,1,2,2,3,2,1,2,1,2,0,1,1,2,1,1,2,2,3,2,1,

%T 2,1,2,1,2,2,3,2,2,3,3,4,3,2,3,2,3,1,2,2,3,2,1,2,1,2,2,3,2,3,2,0,1,1,

%U 2,1,1,2,2,3,2,1,2,1,2,1,2,2,3,2,2,3,3,4,3,2,3,2,3,1,2,2,3,2,1,2,1,2

%N a(n) = number of nodes with nonzero even distance to the root in the n-th plane general tree encoded by A014486(n).

%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 is one node marked with 'e', thus a(27)=1.

%o (Scheme:) (define (A126304 n) (*A126304 (A014486->parenthesization (A014486 n))))

%o (define (*A126304 s) (cond ((null? s) 0) (else (apply + (map *A126303 s)))))

%Y a(n) = A126305(n)-1. Cf. A126303. Scheme-function A014486->parenthesization given in A014486.

%K nonn

%O 0,8

%A _Antti Karttunen_, Jan 02 2007