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A290744 Maximum number of distinct Lyndon factors that can appear in words of length n over an alphabet of size 5. 2
5, 6, 8, 11, 15, 19, 24, 30, 37, 45, 53, 62, 72, 83, 95, 107, 120, 134, 149, 165, 181, 198, 216, 235, 255, 275, 296, 318, 341, 365, 389, 414, 440, 467, 495, 523, 552, 582, 613, 645, 677, 710, 744, 779, 815, 851, 888, 926, 965, 1005, 1045, 1086, 1128, 1171, 1215 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..55.

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=5, m=floor(n/s), p=n-m*s. - Andrew Howroyd, Aug 14 2017

Conjectures from Colin Barker, Oct 03 2017: (Start)

G.f.: x*(5 - 4*x + x^2 + x^3 + x^4 - 5*x^5 + 5*x^6) / ((1 - x)^3*(1 + x + x^2 + x^3 + x^4)).

a(n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7) for n>6.

(End)

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)(5); \\ Andrew Howroyd, Aug 14 2017

CROSSREFS

Cf. A290743, A290745, A290747.

Sequence in context: A332549 A091091 A262161 * A120151 A022937 A030742

Adjacent sequences: A290741 A290742 A290743 * A290745 A290746 A290747

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 11 2017

EXTENSIONS

a(11)-a(55) from Andrew Howroyd, Aug 14 2017

STATUS

approved

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Last modified December 2 20:59 EST 2022. Contains 358510 sequences. (Running on oeis4.)