cp's OEIS Frontend

A290745 Maximum number of distinct Lyndon factors that can appear in words of length n over an alphabet of size 10.

%I A290745 #23 Sep 08 2022 08:46:19
%S A290745 10,11,13,16,20,25,31,38,46,55,64,74,85,97,110,124,139,155,172,190,
%T A290745 208,227,247,268,290,313,337,362,388,415,442,470,499,529,560,592,625,
%U A290745 659,694,730,766,803,841,880,920,961,1003,1046,1090,1135
%N A290745 Maximum number of distinct Lyndon factors that can appear in words of length n over an alphabet of size 10.
%H A290745 Vincenzo Librandi, <a href="/A290745/b290745.txt">Table of n, a(n) for n = 1..1000</a>
%H A290745 Amy Glen, Jamie Simpson, and W. F. Smyth, <a href="https://doi.org/10.37236/6915">Counting Lyndon Factors</a>, Electronic Journal of Combinatorics 24(3) (2017), #P3.28.
%H A290745 Ryo Hirakawa, Yuto Nakashima, Shunsuke Inenaga, and Masayuki Takeda, <a href="https://arxiv.org/abs/2106.01190">Counting Lyndon Subsequences</a>, arXiv:2106.01190 [math.CO], 2021. See MDF(n, s).
%F A290745 a(n) = binomial(n+1,2) - (s-p)*binomial(m+1,2) - p*binomial(m+2,2) + s where s=10, m=floor(n/s), p=n-m*s. - _Andrew Howroyd_, Aug 14 2017
%F A290745 G.f.: x*(10 - 9*x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 - 10*x^10 + 10*x^11) / ((1 - x)^3*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)) (conjectured). - _Colin Barker_, Oct 03 2017
%t A290745 Table[(Binomial[n+1, 2] - (10 - (n-10 Floor[n/10])) Binomial[Floor[n/10]+1, 2]- (n-10 Floor[n/10]) Binomial[Floor[n/10]+2, 2]+10), {n, 60}] (* _Vincenzo Librandi_, Oct 04 2017 *)
%o A290745 (PARI) a(n)=(s->my(m=n\s, p=n%s); binomial(n+1, 2)-(s-p)*binomial(m+1, 2)-p*binomial(m+2, 2)+s)(10); \\ _Andrew Howroyd_, Aug 14 2017
%o A290745 (Magma) [Binomial(n+1,2)-(10-(n-10*Floor(n/10)))*Binomial(Floor(n/10)+1,2)-(n-10*Floor(n/10))*Binomial(Floor(n/10)+2,2)+ 10: n in [1..50]]; // _Vincenzo Librandi_, Oct 04 2017
%Y A290745 Cf. A290743, A290744.
%K A290745 nonn
%O A290745 1,1
%A A290745 _N. J. A. Sloane_, Aug 11 2017
%E A290745 a(11)-a(50) from _Andrew Howroyd_, Aug 14 2017