This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A137747 #26 Jun 08 2025 13:44:01
%S A137747 0,0,0,0,0,0,0,1,7,34,143,555,2050,7343,25809,89642,308986,1059786,
%T A137747 3623524,12365973,42160774,143701920,489891138,1670965268,5703849531,
%U A137747 19488123707,66652727622,228212500386,782258463295,2684464903407,9222805414564,31722184749945,109232421818064
%N A137747 Number of different strings of length n obtained from "abcdefg" by iteratively duplicating any substring.
%C A137747 See A137743 for more comments.
%H A137747 <a href="/index/Do#repeat">Index entries for doubling substrings</a>
%e A137747 a(k) = 0 for k<7, since no shorter string can be obtained by duplication of substrings.
%e A137747 a(7) = 1 = #{abcdefg},
%e A137747 a(8) = 7 = #{aabcdefg, abbcdefg, abccdefg, abcddefg, abcdeefg, abcdeffg, abcdefgg},
%e A137747 a(9) = 8*(8+1)/2-2 = 34:
%e A137747 for each letter we have one string of the form aaabcdefg;
%e A137747 for each 2-element subset {a,b}, {a,c}, ... we have the string with each of these two letters duplicated (i.e., aabbcdefg, aabccdefg, ...);
%e A137747 and for each of ab,bc,cd,...,fg we have the string with this substring duplicated (ababcdefg,...,abcdefgfg).
%e A137747 (See A137746 for the pattern.)
%o A137747 (PARI) A135473(14,7) /* function defined in A137743 */
%Y A137747 Cf. A137740-A137743, A135473, A137744-A137748.
%K A137747 nonn
%O A137747 0,9
%A A137747 _M. F. Hasler_, Feb 10 2008
%E A137747 a(15)-a(20) from _Lars Blomberg_, Jan 12 2013
%E A137747 a(21) from _Michael S. Branicky_, Jan 07 2021
%E A137747 a(22)-a(23) from _Bert Dobbelaere_, Jun 11 2024
%E A137747 a(24)-a(32) from _Martin Fuller_, Jun 08 2025