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A317849 Number of states of the Finite State Automaton Gn accepting the language of maximal (or minimal) lexicographic representatives of elements in the positive braid monoid An. 0
1, 5, 18, 56, 161, 443, 1190, 3156, 8315, 21835, 57246, 149970, 392743, 1028351, 2692416, 7049018, 18454775, 48315461, 126491780, 331160070, 866988641, 2269806085, 5942429868, 15557483796, 40730021821, 106632581993, 279167724510, 730870591916, 1913444051645, 5009461563455 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..30.

Ramón Flores, Juan González-Meneses, On lexicographic representatives in braid monoids, arXiv:1808.02755 [math.GR], 2018.

Volker Gebhardt, Juan González-Meneses, Generating random braids, J. Comb. Th. A 120 (1), 2013, 111-128.

FORMULA

a(n) = Sum_{i=1..n} (binomial(n+1-i, 2)+1)*Fibonacci(2*i).

Conjecture: g.f. -x*(1-x+x^2) / ( (x^2-3*x+1)*(x-1)^3 ). a(n) = 2*A001519(n+1) -n*(n+1)/2 -2 = 2*A001519(n+1)-A152948(n+2). - R. J. Mathar, Aug 17 2018

MATHEMATICA

Table[Sum[(Binomial[n + 1 - k, 2] + 1) Fibonacci[2 k], {k, n}], {n, 30}] (* Vincenzo Librandi, Aug 09 2018 *)

PROG

(PARI) a(n) = sum(i=1, n, (binomial(n+1-i, 2)+1)*fibonacci(2*i));

(MAGMA) [&+[(Binomial(n+1-k, 2)+1)*Fibonacci(2*k): k in [1..n]]: n in [1..30]]; // Vincenzo Librandi, Aug 09 2018

(GAP) List([1..30], n->Sum([1..n], i->(Binomial(n+1-i, 2)+1)*Fibonacci(2*i))); # Muniru A Asiru, Aug 09 2018

CROSSREFS

Sequence in context: A099450 A145129 A001793 * A307572 A093374 A258109

Adjacent sequences:  A317846 A317847 A317848 * A317850 A317851 A317852

KEYWORD

nonn

AUTHOR

Michel Marcus, Aug 09 2018

STATUS

approved

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Last modified April 23 02:15 EDT 2019. Contains 322380 sequences. (Running on oeis4.)