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 A135017 #13 Jun 06 2025 14:48:18 %S A135017 0,0,1,0,2,1,3,5,7,15,20,48,60,156,205,489,761,1572,2796,5357,10174, %T A135017 19021,37272,69375,137759,258444,513696,976890,1934900,3727164, %U A135017 7358675,14316861,28217028,55288907,108942267,214462953,422973649,835145308,1649638479,3263689911,6457465848,12795025182,25355766038,50304700910 %N A135017 a(n) is number of strings of length n that can be obtained by starting with abc and repeatedly doubling any substring in place and then discarding any string that contains two successive equal letters. %C A135017 These strings may be regarded as the "primitive" strings among those enumerated by A135473. %C A135017 Equals the inverse binomial transform of A135473. %H A135017 <a href="/index/Do#repeat">Index entries for doubling substrings</a> %F A135017 Empirically, grows like 2^n. %e A135017 n=3: abc %e A135017 n=4: - %e A135017 n=5: ababc, abcbc %e A135017 n=6: abcabc %e A135017 n=7: abababc, ababcbc, abcbcbc %Y A135017 Cf. A135473. %K A135017 nonn %O A135017 1,5 %A A135017 _David Applegate_ and _N. J. A. Sloane_, Feb 12 2008 %E A135017 Extended to 37 terms by _David Applegate_, Feb 16 2008 %E A135017 a(38)-a(44) by _Martin Fuller_, Jun 06 2025