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.

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.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Rémy Sigrist, PARI program

Wikipedia, Infiltration product.

Index entries for sequences related to binary expansion of n

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

Cf. A000096, A191755, A193020.

Sequence in context: A119435 A352783 A193972 * A332357 A305126 A044043

Adjacent sequences: A361395 A361396 A361397 * A361399 A361400 A361401

Keyword

nonn,base

Author

Rémy Sigrist, Mar 10 2023

Status

approved