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A317849
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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.
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0
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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
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = Sum_{i=1..n} (binomial(n+1-i, 2)+1)*Fibonacci(2*i).
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MATHEMATICA
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Table[Sum[(Binomial[n + 1 - k, 2] + 1) Fibonacci[2 k], {k, n}], {n, 30}] (* Vincenzo Librandi, Aug 09 2018 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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