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 A303117 #20 May 18 2018 20:38:51 %S A303117 1,1,1,2,6,18,62,186,570,1680,4890,14058,40200,114450,325230,923846, %T A303117 2624730,7465410,21260652,60647370,173288724,496014934,1422211494, %U A303117 4084793082,11751102060,33857989968,97696908330,282295318536,816759712080,2366027865810,6861963548198,19922800783578,57902584654650 %N A303117 a(n) is the number of cyclic permutations with at most two descents. %C A303117 The number of cyclic permutations with at most 2 descents is equal to L(3,n)-n*L(2,n) where L(k,n) is the number of primitive necklaces (equivalently, the number of Lyndon words) of length n on k letters. %H A303117 I. M. Gessel and C. Reutenauer, <a href="http://dx.doi.org/10.1016/0097-3165(93)90095-P">Counting permutations with given cycle structure and descent set</a>, J. Combin. Theory, Ser. A, 64, 189-215, (1993). %F A303117 a(n) = A027376(n) - n*A001037(n). %F A303117 a(n) = L(3,n)-n*L(2,n) where L(k,n) is the number of primitive k-ary necklaces (or equivalently, Lyndon words) of length n. %o A303117 (PARI) L2(n) = if(n>1, sumdiv(n, d, moebius(d)*2^(n/d))/n, n+1); \\ A001037 %o A303117 L3(n) = if(n<1, n==0, sumdiv(n, d, moebius(n/d)*3^d)/n); \\ A027376 %o A303117 a(n) = L3(n)-n*L2(n); \\ _Michel Marcus_, May 17 2018 %Y A303117 Cf. A027376, A001037. %K A303117 nonn %O A303117 0,4 %A A303117 _Kassie Archer_, Apr 18 2018