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A126303
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.
4
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, 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, 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
OFFSET
0,3
EXAMPLE
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.
.......o
.......|
.......e
.......|
...o.o.o
....\|/.
.....*..
there are four nodes marked with 'o', thus a(27)=4.
PROG
(MIT Scheme:) (define (A126303 n) (*A126303 (A014486->parenthesization (A014486 n))))
(define (*A126303 s) (cond ((null? s) 0) (else (fold-left (lambda (x y) (+ x 1 (*A126304 y))) 0 s))))
CROSSREFS
a(n) = A072643(n)-A126305(n). Cf. A126304. Scheme-function A014486->parenthesization given in A014486.
Sequence in context: A090000 A109082 A324923 * A306467 A157810 A072339
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 02 2007
STATUS
approved