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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.
2
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, 10, 13, 5, 1, 6, 19, 46, 29, 59, 96, 69, 24, 44, 106, 156, 82, 66, 92, 42, 10, 15, 45, 88, 52, 75, 118, 75, 24, 20, 45, 58, 29, 15, 19, 6, 1, 7, 26, 73, 49, 114, 194
OFFSET
0,3
COMMENTS
a(n) gives the number of ways to zero n bit by bit.
FORMULA
a(n) = 1 iff n belongs to A000225.
a(2^k) = k + 1 for any k >= 0.
a(n) <= A368070(n).
EXAMPLE
For n = 5:
- the binary expansion of 5 is "101",
- we have the following appropriate sequences:
(5, 3, 1, 0)
(5, 2, 1, 0)
(5, 2, 0)
(5, 1, 0)
- hence a(5) = 4.
PROG
(PARI) See Links section.
CROSSREFS
See A060351 and A368070 for similar sequences.
Cf. A000225.
Sequence in context: A050273 A182511 A187064 * A193020 A301471 A237124
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Dec 10 2023
STATUS
approved