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A368070
a(n) is the number of sequences of binary words (w_1, ..., w_k) such that w_1 corresponds to the binary expansion of n (without leading zeros), for m = 1..k-1, w_{m+1} is obtained by removing one bit from w_m, and w_k is the empty word.
2
1, 1, 2, 1, 3, 5, 3, 1, 4, 11, 16, 9, 6, 9, 4, 1, 5, 19, 40, 26, 35, 61, 40, 14, 10, 26, 35, 19, 10, 14, 5, 1, 6, 29, 78, 55, 99, 181, 132, 50, 64, 181, 272, 155, 111, 169, 78, 20, 15, 55, 111, 71, 90, 155, 99, 34, 20, 50, 64, 34, 15, 20, 6, 1, 7, 41, 133, 99
OFFSET
0,3
COMMENTS
Leading zeros may appear in binary words w_2, ..., w_{k-1}.
a(n) gives the number of ways to erase the binary expansion of n bit by bit.
FORMULA
a(n) = 1 iff n belongs to A000225.
a(2^k) = k + 1 for any k >= 0.
a(n) >= A367019(n).
EXAMPLE
For n = 5:
- the binary expansion of 5 is "101",
- we have the following appropriate sequences of binary words:
("101", "11", "1", "")
("101", "10", "1", "")
("101", "10", "0", "")
("101", "01", "1", "")
("101", "01", "0", "")
- hence a(5) = 5.
PROG
(PARI) See Links section.
CROSSREFS
See A060351 and A367019 for similar sequences.
Cf. A000225.
Sequence in context: A019588 A193953 A201377 * A322942 A060083 A069931
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Dec 10 2023
STATUS
approved