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A090327
Number of rules of a context-free grammar in Chomsky normal form that generates all permutations of n symbols.
2
1, 4, 11, 30, 83, 234, 671, 1950, 5723, 16914, 50231, 149670, 446963, 1336794, 4002191, 11990190, 35937803, 107747874, 323112551, 969075510, 2906702243, 8719058154, 26155077311, 78461037630, 235374724283, 706107395634, 2118288632471, 6354798788550
OFFSET
1,2
FORMULA
a(n) = ceiling[ (5*3^(n-2))/2 + 2^(n-1) - 1/2 ] for n > 1.
G.f.: -x*(2*x^3-2*x^2-2*x+1) / ((x-1)*(2*x-1)*(3*x-1)). - Colin Barker, Jan 15 2015
a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3) for n >= 5. - Robert Israel, Jan 15 2015
EXAMPLE
S -> AD | DA | BE | EB, D -> BC | CB, E -> AC | CA, A -> a, B -> b, C-> c; so a(3)=11.
MAPLE
f:= gfun:-rectoproc({a(n) = 6*a(n-1)-11*a(n-2)+6*a(n-3), a(1)=1, a(2)=4, a(3)=11, a(4)=30}, a(n), 'remember'):
seq(f(n), n=1..100); # Robert Israel, Jan 15 2015
MATHEMATICA
f[n_] := Ceiling[5/2*3^(n - 2) + 2^(n - 1) - 1/2]; Table[ f[n], {n, 2, 27}] (* Robert G. Wilson v, Jan 30 2004 *)
PROG
(PARI) Vec(-x*(2*x^3-2*x^2-2*x+1)/((x-1)*(2*x-1)*(3*x-1)) + O(x^100)) \\ Colin Barker, Jan 15 2015
CROSSREFS
Sequence in context: A019496 A021006 A078141 * A183118 A183125 A183123
KEYWORD
nonn,easy
AUTHOR
Peter R. J. Asveld, Jan 27 2004
EXTENSIONS
More terms from Robert G. Wilson v, Jan 30 2004
STATUS
approved