A137744 - OEIS

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 (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..23.` `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	`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` `a(22)-a(23) from Bert Dobbelaere, Jun 10 2024`
	STATUS	`approved`