cp's OEIS Frontend

A137745 Number of different strings of length n obtained from "abcde" by iteratively duplicating any substring.

%I A137745 #22 Jun 07 2025 11:58:22
%S A137745 0,0,0,0,0,1,5,19,66,218,700,2218,6997,22064,69662,220395,699090,
%T A137745 2224114,7098773,22733498,73048903,235504760,761689193,2471105355,
%U A137745 8040439771,26235143469,85831045851,281519068056,925596771195,3050264328190,10074150332305,33341934697311,110571437129989
%N A137745 Number of different strings of length n obtained from "abcde" by iteratively duplicating any substring.
%C A137745 See A137743 for more comments.
%H A137745 <a href="/index/Do#repeat">Index entries for doubling substrings</a>
%e A137745 a(k) = 0 for k<5, since no shorter string can be obtained by duplicating a substring.
%e A137745 a(5) = # { abcde },
%e A137745 a(6) = # { aabcde, abbcde, abccde, abcdde, abcdee },
%e A137745 a(7) = # { aaabcde, aabbcde, aabccde, aabcdde, aabcdee, ababcde, abbbcde, abbccde, abbcdde, abbcdee, abcbcde, abcccde, abccdde, abccdee, abcdcde, abcddde, abcddee, abcdede, abcdeee }
%o A137745 (PARI) A135473(13,5) /* function defined in A137743...*/
%Y A137745 Cf. A137740-A137743, A135473, A137744-A137748.
%K A137745 nonn
%O A137745 0,7
%A A137745 _M. F. Hasler_, Feb 10 2008
%E A137745 a(14)-a(19) from _Lars Blomberg_, Jan 12 2013
%E A137745 a(20)-a(21) from _Michael S. Branicky_, Jan 05 2021
%E A137745 a(22)-a(23) from _Bert Dobbelaere_, Jun 10 2024
%E A137745 a(24)-a(32) from _Martin Fuller_, Jun 07 2025