cp's OEIS Frontend

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

%I A277335 #17 Apr 24 2025 17:06:08
%S A277335 0,3,6,12,15,24,27,30,48,51,54,60,63,96,99,102,108,111,120,123,126,
%T A277335 192,195,198,204,207,216,219,222,240,243,246,252,255,384,387,390,396,
%U A277335 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
%N A277335 Fibbinary numbers multiplied by three: a(n) = 3*A003714(n); Numbers where all 1-bits occur in runs of even length.
%C A277335 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
%H A277335 Antti Karttunen, <a href="/A277335/b277335.txt">Table of n, a(n) for n = 0..17711</a>
%H A277335 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A277335 a(n) = 3*A003714(n).
%t A277335 3 Select[Range[300], BitAnd[#, 2 #]==0 &] (* _Vincenzo Librandi_, Sep 12 2017 *)
%o A277335 (Scheme) (define (A277335 n) (* 3 (A003714 n)))
%o A277335 (Python)
%o A277335 def A277335(n):
%o A277335     tlist, s = [1,2], 0
%o A277335     while tlist[-1]+tlist[-2] <= n: tlist.append(tlist[-1]+tlist[-2])
%o A277335     for d in tlist[::-1]:
%o A277335         s <<= 1
%o A277335         if d <= n:
%o A277335             s += 1
%o A277335             n -= d
%o A277335     return 3*s # _Chai Wah Wu_, Apr 24 2025
%Y A277335 Cf. A003714.
%Y A277335 Positions of odd terms in A106737.
%Y A277335 Cf. also A001196 (a subsequence).
%K A277335 nonn,base
%O A277335 0,2
%A A277335 _Antti Karttunen_, Oct 18 2016