login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A137744 Number of different strings of length n obtained from "abcd" by iteratively duplicating any substring. 12
0, 0, 0, 0, 1, 4, 13, 40, 119, 348, 1014, 2966, 8726, 25820, 76823, 229814, 691186, 2089850, 6351448, 19398726, 59525641, 183462778 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

See A137743 for more comments.

LINKS

Table of n, a(n) for n=0..21.

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: A191132 A119915 A307577 * A027130 A027121 A238846

Adjacent sequences:  A137741 A137742 A137743 * A137745 A137746 A137747

KEYWORD

more,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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 14 01:36 EDT 2019. Contains 327994 sequences. (Running on oeis4.)