A209642 - OEIS

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A209642

A014486-codes for rooted plane trees where non-leaf branching can occur only at the leftmost branch of any level, but nowhere else. Reflected from the corresponding rightward branching codes in A071162, thus not in ascending order.

0, 2, 10, 12, 42, 50, 52, 56, 170, 202, 210, 226, 212, 228, 232, 240, 682, 810, 842, 906, 850, 914, 930, 962, 852, 916, 932, 964, 936, 968, 976, 992, 2730, 3242, 3370, 3626, 3402, 3658, 3722, 3850, 3410, 3666, 3730, 3858, 3746, 3874, 3906, 3970, 3412, 3668, 3732, 3860, 3748, 3876, 3908, 3972, 3752, 3880, 3912, 3976, 3920, 3984, 4000, 4032

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

Like with A071162, a(n) can be computed directly from the binary expansion of n. (See the Scheme function given). However, the function is not monotone. A209641 gives the same terms in ascending order.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..32767

FORMULA

a(n) = A056539(A071162(n)) = A036044(A071162(n)). (See also the given Scheme-function).

PROG

(Scheme) (define (A209642 n) (let loop ((n n) (s 0) (i 1)) (cond ((zero? n) s) ((even? n) (loop (/ n 2) (+ (* 4 s) 1) (* i 4))) (else (loop (/ (- n 1) 2) (* 2 (+ s i)) (* i 4))))))

(Python)

def a(n):

s=0

i=1

while n!=0:

if n%2==0:

n//=2

s=4*s + 1

else:

n=(n - 1)//2

s=(s + i)*2

i*=4