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 A303117 a(n) is the number of cyclic permutations with at most two descents. 1
 1, 1, 1, 2, 6, 18, 62, 186, 570, 1680, 4890, 14058, 40200, 114450, 325230, 923846, 2624730, 7465410, 21260652, 60647370, 173288724, 496014934, 1422211494, 4084793082, 11751102060, 33857989968, 97696908330, 282295318536, 816759712080, 2366027865810, 6861963548198, 19922800783578, 57902584654650 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 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. LINKS Table of n, a(n) for n=0..32. I. M. Gessel and C. Reutenauer, Counting permutations with given cycle structure and descent set, J. Combin. Theory, Ser. A, 64, 189-215, (1993). FORMULA a(n) = A027376(n) - n*A001037(n). 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. PROG (PARI) L2(n) = if(n>1, sumdiv(n, d, moebius(d)*2^(n/d))/n, n+1); \\ A001037 L3(n) = if(n<1, n==0, sumdiv(n, d, moebius(n/d)*3^d)/n); \\ A027376 a(n) = L3(n)-n*L2(n); \\ Michel Marcus, May 17 2018 CROSSREFS Cf. A027376, A001037. Sequence in context: A346490 A177473 A177471 * A150052 A262590 A150053 Adjacent sequences: A303114 A303115 A303116 * A303118 A303119 A303120 KEYWORD nonn AUTHOR Kassie Archer, Apr 18 2018 STATUS approved

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Last modified June 21 03:54 EDT 2024. Contains 373540 sequences. (Running on oeis4.)