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A361398
An infiltration of two words, say x and y, is a shuffle of x and y optionally followed by replacements of pairs of consecutive equal symbols, say two d's, one of which comes from x and the other from y, by a single d (that cannot be part of another replacement); a(n) is the number of distinct infiltrations of the word given by the binary representation of n with itself.
3
1, 2, 5, 3, 9, 12, 9, 4, 14, 28, 30, 21, 19, 21, 14, 5, 20, 53, 68, 60, 55, 74, 68, 32, 34, 60, 55, 36, 34, 32, 20, 6, 27, 89, 126, 134, 120, 181, 196, 108, 88, 181, 183, 136, 151, 164, 126, 45, 55, 134, 151, 129, 107, 136, 120, 54, 69, 108, 88, 54, 55, 45, 27
OFFSET
0,2
COMMENTS
Leading zeros in binary expansions are ignored.
See A191755 for the definition of a shuffle.
FORMULA
a(n) >= A193020(n).
a(2^k - 1) = k + 1 for any k >= 0.
a(2^k) = A000096(k + 1) for any k >= 0.
EXAMPLE
For n = 2:
- the binary expansion of 2 is "10",
- we have essentially the following infiltrations:
x 10 10 1 0 10 1 0
y 10 1 0 10 10 1 0
-- --- --- ---- ----
infiltration 10 100 110 1010 1100
- so a(2) = 5.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Mar 10 2023
STATUS
approved