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

0,2

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

Crossrefs

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

Sequence in context: A071162 A075165 A209641 * A061855 A358524 A144145

Adjacent sequences: A209639 A209640 A209641 * A209643 A209644 A209645

Keyword

nonn,easy

Author

Antti Karttunen, Mar 11 2012

Status

approved