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A293722
Number of distinct nonempty subsequences of the binary expansion of n.
2
1, 1, 3, 2, 5, 6, 5, 3, 7, 10, 11, 9, 8, 9, 7, 4, 9, 14, 17, 15, 16, 19, 17, 12, 11, 15, 16, 13, 11, 12, 9, 5, 11, 18, 23, 21, 24, 29, 27, 20, 21, 29, 32, 27, 25, 28, 23, 15, 14, 21, 25, 22, 23, 27, 24, 17, 15, 20, 21, 17, 14, 15, 11, 6, 13, 22, 29, 27, 32, 39, 37
OFFSET
0,3
COMMENTS
The subsequence does not need to consist of adjacent terms.
LINKS
FORMULA
a(2^n) = 2n + 1.
a(2^n-1) = n if n>0.
a(n) = A293170(n) - 1. - Andrew Howroyd, Apr 27 2020
EXAMPLE
a(4) = 5 because 4 = 100_2, and the distinct subsequences of 100 are 0, 1, 00, 10, 100.
Similarly a(7) = 3, because 7 = 111_2, and 111 has only three distinct subsequences: 1, 11, 111.
a(9) = 10: 9 = 1001_2, and we get 0, 1, 00, 01, 10, 11, 001, 100, 101, 1001.
PROG
(Python)
def a(n):
if n == 0: return 1
r, l = 1, [0, 0]
while n:
r, l[n%2] = 2*r - l[n%2], r
n >>= 1
return r - 1
CROSSREFS
Cf. A141297.
If the empty subsequence is also counted, we get A293170.
Sequence in context: A057028 A195112 A276618 * A364254 A153152 A153153
KEYWORD
nonn,base,easy
AUTHOR
Orson R. L. Peters, Oct 15 2017
EXTENSIONS
Terms a(50) and beyond from Andrew Howroyd, Apr 27 2020
STATUS
approved