A277335 Fibbinary numbers multiplied by three: a(n) = 3*A003714(n); Numbers where all 1-bits occur in runs of even length.

0, 3, 6, 12, 15, 24, 27, 30, 48, 51, 54, 60, 63, 96, 99, 102, 108, 111, 120, 123, 126, 192, 195, 198, 204, 207, 216, 219, 222, 240, 243, 246, 252, 255, 384, 387, 390, 396, 399, 408, 411, 414, 432, 435, 438, 444, 447, 480, 483, 486, 492, 495, 504, 507, 510, 768, 771, 774, 780, 783, 792, 795, 798, 816, 819, 822, 828, 831, 864, 867, 870, 876, 879, 888

Offset: 0

Author

Antti Karttunen, Oct 18 2016

Keywords

• nonn
• base

Comments

The positive entries are the viabin numbers of integer partitions into even parts. The viabin number of an integer partition is defined in the following way. Consider the southeast border of the Ferrers board of the integer partition and consider the binary number obtained by replacing each east step with 1 and each north step, except the last one, with 0. The corresponding decimal form is, by definition, the viabin number of the given integer partition. "Viabin" is coined from "via binary". For example, consider the integer partition [6,4,4,2]. The southeast border of its Ferrers board yields 110110011, leading to the viabin number 435 (a term of the sequence). - Emeric Deutsch, Sep 11 2017

Links

• Antti Karttunen, Table of n, a(n) for n = 0..17711
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A003714.

Positions of odd terms in A106737.

Cf. also A001196 (a subsequence).

Programs

Mathematica

3 Select[Range[300], BitAnd[#, 2 #]==0 &] (* Vincenzo Librandi, Sep 12 2017 *)

Python

def A277335(n):
    tlist, s = [1,2], 0
    while tlist[-1]+tlist[-2] <= n: tlist.append(tlist[-1]+tlist[-2])
    for d in tlist[::-1]:
        s <<= 1
        if d <= n:
            s += 1
            n -= d
    return 3*s # Chai Wah Wu, Apr 24 2025

Scheme

(define (A277335 n) (* 3 (A003714 n)))

Formula

a(n) = 3*A003714(n).