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

Offset: 0

Author

Antti Karttunen, Mar 11 2012

Keywords

• nonn
• easy

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

Crossrefs

a(n) = A209641(A209861(n)).

Programs

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
    return s
print([a(n) for n in range(101)]) # Indranil Ghosh, May 25 2017, translated from Antti Karttunen's SCHEME code

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))))))

Formula

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