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A290745 Maximum number of distinct Lyndon factors that can appear in words of length n over an alphabet of size 10. 3
10, 11, 13, 16, 20, 25, 31, 38, 46, 55, 64, 74, 85, 97, 110, 124, 139, 155, 172, 190, 208, 227, 247, 268, 290, 313, 337, 362, 388, 415, 442, 470, 499, 529, 560, 592, 625, 659, 694, 730, 766, 803, 841, 880, 920, 961, 1003, 1046, 1090, 1135 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Amy Glen, Jamie Simpson, and W. F. Smyth, Counting Lyndon Factors, Electronic Journal of Combinatorics 24(3) (2017), #P3.28.

Ryo Hirakawa, Yuto Nakashima, Shunsuke Inenaga, and Masayuki Takeda, Counting Lyndon Subsequences, arXiv:2106.01190 [math.CO], 2021. See MDF(n, s).

FORMULA

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

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

MATHEMATICA

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 *)

PROG

(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

(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

CROSSREFS

Cf. A290743, A290744.

Sequence in context: A153194 A175224 A106439 * A121263 A121295 A121296

Adjacent sequences:  A290742 A290743 A290744 * A290746 A290747 A290748

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 11 2017

EXTENSIONS

a(11)-a(50) from Andrew Howroyd, Aug 14 2017

STATUS

approved

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Last modified October 23 08:40 EDT 2021. Contains 348211 sequences. (Running on oeis4.)