cp's OEIS Frontend

A367019 a(n) is the number of strictly decreasing sequences (w_1, ..., w_k) such that w_1 = n, for m = 1..k-1, w_{m+1} is obtained by removing one significant binary digit from w_m, and w_k = 0.

%I A367019 #34 Dec 22 2023 09:24:29
%S A367019 1,1,2,1,3,4,3,1,4,8,12,6,6,8,4,1,5,13,26,15,25,38,25,8,10,22,30,15,
%T A367019 10,13,5,1,6,19,46,29,59,96,69,24,44,106,156,82,66,92,42,10,15,45,88,
%U A367019 52,75,118,75,24,20,45,58,29,15,19,6,1,7,26,73,49,114,194
%N A367019 a(n) is the number of strictly decreasing sequences (w_1, ..., w_k) such that w_1 = n, for m = 1..k-1, w_{m+1} is obtained by removing one significant binary digit from w_m, and w_k = 0.
%C A367019 a(n) gives the number of ways to zero n bit by bit.
%H A367019 Rémy Sigrist, <a href="/A367019/b367019.txt">Table of n, a(n) for n = 0..8192</a>
%H A367019 Rémy Sigrist, <a href="/A367019/a367019.gp.txt">PARI program</a>
%H A367019 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A367019 a(n) = 1 iff n belongs to A000225.
%F A367019 a(2^k) = k + 1 for any k >= 0.
%F A367019 a(n) <= A368070(n).
%e A367019 For n = 5:
%e A367019 - the binary expansion of 5 is "101",
%e A367019 - we have the following appropriate sequences:
%e A367019      (5, 3, 1, 0)
%e A367019      (5, 2, 1, 0)
%e A367019      (5, 2, 0)
%e A367019      (5, 1, 0)
%e A367019 - hence a(5) = 4.
%o A367019 (PARI) See Links section.
%Y A367019 See A060351 and A368070 for similar sequences.
%Y A367019 Cf. A000225.
%K A367019 nonn,base
%O A367019 0,3
%A A367019 _Rémy Sigrist_, Dec 10 2023