A137744 Number of different strings of length n obtained from "abcd" by iteratively duplicating any substring.

0, 0, 0, 0, 1, 4, 13, 40, 119, 348, 1014, 2966, 8726, 25820, 76823, 229814, 691186, 2089850, 6351448, 19398726, 59525641, 183462778, 567794458, 1764118964, 5501252365, 17214902088, 54047671324, 170218070930, 537678825668, 1703200355646, 5409721322664, 17226400794280

Offset

0,6

Comments

See A137743 for more comments.

Links

Martin Fuller, Table of n, a(n) for n = 0..34

Index entries for doubling substrings

Example

a(4) = # { abcd },
a(5) = # { aabcd, abbcd, abccd, abcdd },
a(6) = # { aaabcd, aabbcd, aabccd, aabcdd, ababcd, abbbcd, abbccd, abbcdd, abcbcd, abcccd, abccdd, abcdcd, abcddd }

Prog

(PARI) A135473(12, 4)
(Python)
def process(s, n, catalog, cache):
    l=len(s)
    if l==n:
        catalog.add(s)
        return
    if s in cache:
        return
    cache.add(s)
    for x in range(l):
        for y in range(x+1, min(x+n-l, l)+1):
            process(s[:y]+s[x:], n, catalog, cache)
def A137744(n):
    catalog=set()
    cache=set()
    process("abcd", n, catalog, cache)
    return len(catalog)
# Bert Dobbelaere, Nov 01 2018

Crossrefs

Cf. A137740-A137743, A135473, A137745-A137748.

Sequence in context: A360606 A119915 A307577 * A027130 A027121 A238846

Adjacent sequences: A137741 A137742 A137743 * A137745 A137746 A137747

Keyword

nonn

Author

M. F. Hasler, Feb 10 2008

Extensions

a(13)-a(19) from Lars Blomberg, Jan 12 2013

a(20)-a(21) from Bert Dobbelaere, Nov 01 2018

a(22)-a(23) from Bert Dobbelaere, Jun 10 2024

a(24) onwards from Martin Fuller, Jun 07 2025

Status

approved